Subgroups — C₄×#15689320 #26222470

Order 12032.

1152 conjugacy classes of subgroups.

The subgroup lattice has 548 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	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244316	C₂	1	1	yes	maximal, characteristic
5	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244012	C₂	1	2	yes	maximal, complemented
7	#20243746	C₂	1	2	yes	maximal, complemented
8	#20243390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093945	C₂	1	2	yes	maximal, complemented
11	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625335	C₂²	1	2	yes	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
16	#15689320	C₄	1	8	yes	direct product factor
17	C₄×#10625335	—	2	8	no	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093947	C₂²	1	2	yes	—
22	C₂×#13093945	C₂²	1	2	yes	—
23	C₂×#13093945	C₂²	1	2	yes	—
24	C₂×#13093945	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₄×Dic₄₇⋊C₄	—	2	1	no	—
27	C₄×Dic₄₇⋊C₄	—	2	1	no	—
28	C₄×Dic₄₇⋊C₄	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄²×Dic₄₇	—	2	1	no	—
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	—	2	1	no	—
38	C₂×C₄×D₄×C₄₇	—	2	1	no	—
39	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#390	—	2	1	no	—
41	C₄₇×#390	—	2	1	no	—
42	C₄₇×#390	C₂²	1	2	yes	—
43	C₄₇×#384	C₂²	1	1	yes	characteristic
44	C₄³×C₄₇	C₂²	1	1	yes	characteristic
45	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
46	C₂×#10625335	—	2	4	no	—
47	C₂×#10625335	—	2	4	no	—
48	C₂×#10625335	C₂×C₄	1	8	yes	complemented
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₄×Dic₉₄	—	2	2	no	—
52	C₄×Dic₉₄	—	2	2	no	—
53	C₄×Dic₉₄	—	2	2	no	—
54	C₄×Dic₉₄	—	2	2	no	—
55	C₄×Dic₉₄	C₂×C₄	1	4	yes	complemented
56	C₄×Dic₉₄	D₄	1	4	yes	complemented
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	—	2	1	no	—
61	C₂×Dic₄₇⋊C₄	—	2	1	no	—
62	C₂×Dic₄₇⋊C₄	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	#13093955	—	2	4	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
72	#13093947	—	2	4	no	—
73	#13093945	—	2	4	no	—
74	#13093945	—	2	4	no	—
75	#13093945	C₂×C₄	1	8	yes	complemented
76	C₄×C₄₇⋊C₈	—	2	4	no	—
77	C₄₇⋊#95	—	2	1	no	—
78	C₄₇⋊#95	—	2	1	no	—
79	C₄₇⋊#95	—	2	1	no	—
80	C₂²×D₄×C₄₇	—	2	1	no	—
81	C₂²×D₄×C₄₇	—	2	1	no	—
82	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₄₇	—	2	2	no	—
84	#127×C₄₇	—	2	2	no	—
85	#127×C₄₇	C₂×C₄	1	4	yes	—
86	C₄×D₄×C₄₇	—	2	4	no	—
87	C₄×D₄×C₄₇	—	2	4	no	—
88	C₄×D₄×C₄₇	—	4	4	no	—
89	C₄×D₄×C₄₇	—	4	4	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
103	C₂⁴×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	—	2	4	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	4	2	no	—
112	C₂×D₄×C₄₇	—	4	2	no	—
113	C₂×D₄×C₄₇	—	4	2	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
118	C₂²×C₄×C₄₇	—	4	4	no	—
119	C₂²×C₄×C₄₇	—	4	4	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²×Dic₄₇	—	2	1	no	—
128	C₂²×Dic₄₇	—	2	1	no	—
129	C₂²×Dic₄₇	—	2	1	no	—
130	C₂²×Dic₄₇	—	2	1	no	—
131	C₂×Dic₉₄	—	2	1	no	—
132	C₂×Dic₉₄	—	2	1	no	—
133	C₂×Dic₉₄	—	2	1	no	—
134	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
135	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
136	C₂×Dic₉₄	#41	1	2	yes	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	4	2	no	—
140	C₄⋊C₄×C₄₇	—	4	2	no	—
141	C₂²⋊C₄×C₄₇	—	4	4	no	—
142	C₂²⋊C₄×C₄₇	—	4	4	no	—
143	C₂²⋊C₄×C₄₇	—	4	4	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	4	1	no	—
149	C₄²×C₄₇	SD₁₆	1	4	yes	complemented
150	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	#41	1	2	yes	—
153	C₄²×C₄₇	#41	1	2	yes	—
154	#10625335	—	2	16	no	—
155	C₄⋊Dic₄₇	—	2	1	no	—
156	C₄⋊Dic₄₇	—	2	1	no	—
157	C₄⋊Dic₄₇	—	2	1	no	—
158	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
159	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
160	C₄⋊Dic₄₇	#41	1	2	yes	—
161	Dic₄₇⋊C₄	—	2	4	no	—
162	Dic₄₇⋊C₄	—	2	4	no	—
163	Dic₄₇⋊C₄	—	2	4	no	—
164	C₄×Dic₄₇	—	2	4	no	—
165	C₄×Dic₄₇	—	2	4	no	—
166	C₄×Dic₄₇	—	2	4	no	—
167	C₄×Dic₄₇	—	4	2	no	—
168	C₄×Dic₄₇	—	4	2	no	—
169	C₄×Dic₄₇	—	4	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	C₂×C₄₇⋊C₈	—	2	2	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	2	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	2	no	—
180	C₂³×C₄₇	—	4	2	no	—
181	C₂³×C₄₇	—	4	2	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	D₄×C₄₇	—	2	4	no	—
185	D₄×C₄₇	—	2	4	no	—
186	D₄×C₄₇	—	4	8	no	—
187	D₄×C₄₇	—	4	2	no	—
188	D₄×C₄₇	—	4	2	no	—
189	D₄×C₄₇	—	4	8	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	8	8	no	—
203	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₄₇	#121	1	2	yes	—
206	C₂×C₄×C₄₇	#121	1	2	yes	—
207	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₄₇	#135	1	2	yes	—
211	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	C₂×Dic₄₇	—	2	2	no	—
222	C₂×Dic₄₇	—	2	2	no	—
223	C₂×Dic₄₇	—	2	2	no	—
224	C₂×Dic₄₇	—	4	1	no	—
225	C₂×Dic₄₇	—	4	1	no	—
226	C₂×Dic₄₇	—	4	1	no	—
227	C₂×Dic₄₇	—	4	1	no	—
228	C₂×Dic₄₇	—	4	1	no	—
229	C₂×Dic₄₇	—	4	1	no	—
230	Dic₉₄	—	2	2	no	—
231	Dic₉₄	—	2	2	no	—
232	Dic₉₄	—	2	2	no	—
233	Dic₉₄	C₄×D₄	1	4	yes	complemented
234	C₄₇⋊C₈	—	2	4	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄×#460	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	4	4	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	8	2	no	—
241	C₂²×C₄₇	—	8	2	no	—
242	C₂²×C₄₇	—	8	2	no	—
243	C₂²×C₄₇	—	8	2	no	—
244	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
246	C₂²×C₄₇	#525	1	1	yes	characteristic
247	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
249	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₄₇	#575	1	1	yes	characteristic
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	2	2	no	—
253	C₄×C₄₇	—	2	2	no	—
254	C₄×C₄₇	—	4	1	no	—
255	C₄×C₄₇	—	8	2	no	—
256	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
257	C₄×C₄₇	#460	1	4	yes	complemented
258	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
260	C₄×C₄₇	#529	1	1	yes	characteristic
261	C₄×C₄₇	#532	1	1	yes	characteristic
262	Dic₄₇	—	2	4	no	—
263	Dic₄₇	—	4	2	no	—
264	Dic₄₇	—	4	2	no	—
265	Dic₄₇	—	4	2	no	—
266	C₂×#460	—	47	1	no	—
267	C₂×C₄×SD₁₆	—	47	2	no	—
268	C₄×#127	D₄₇	1	1	yes	characteristic
269	C₄²×Q₈	—	47	1	no	—
270	#1982	—	47	1	no	—
271	#1948	—	47	1	no	—
272	#1926	—	47	2	no	—
273	#1880	—	47	2	no	—
274	#1803	—	47	1	no	—
275	C₄×C₄⋊C₈	—	47	1	no	—
276	C₄×#102	—	47	2	no	—
277	C₂×C₄₇	—	8	4	no	—
278	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
279	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
280	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
282	C₂×C₄₇	#3035	1	1	yes	characteristic
283	C₂×C₄₇	#3103	1	1	yes	characteristic
284	C₂×C₄₇	#3106	1	1	yes	characteristic
285	C₂²×SD₁₆	—	47	2	no	—
286	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
287	C₂×C₄×Q₈	—	47	1	no	—
288	C₂×C₄×Q₈	—	47	1	no	—
289	C₂×C₄×Q₈	—	47	1	no	—
290	C₂×C₄×D₄	—	2	1	no	—
291	C₂×C₄×D₄	—	2	1	no	—
292	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
293	#460	—	47	8	no	—
294	C₄×SD₁₆	—	94	8	no	—
295	C₂×#106	—	47	2	no	—
296	C₂×C₄⋊C₈	—	47	1	no	—
297	C₂×C₄⋊C₈	—	47	1	no	—
298	C₂×#103	—	47	2	no	—
299	C₂×#102	—	47	2	no	—
300	C₂×#102	—	47	2	no	—
301	C₂×#102	—	47	2	no	—
302	C₂×C₄×C₈	—	47	2	no	—
303	#390	—	2	1	no	—
304	#390	—	2	1	no	—
305	#390	C₂×D₄₇	1	2	yes	—
306	#384	C₂×D₄₇	1	1	yes	characteristic
307	C₄×C₄⋊C₄	—	47	1	no	—
308	C₄×C₄⋊C₄	—	47	1	no	—
309	C₄×C₄⋊C₄	—	47	1	no	—
310	C₄×C₄⋊C₄	—	94	1	no	—
311	C₄×C₄⋊C₄	—	94	1	no	—
312	C₄×C₄⋊C₄	—	94	1	no	—
313	C₄³	—	94	1	no	—
314	C₄³	C₂×D₄₇	1	1	yes	characteristic
315	#340	—	47	2	no	—
316	#340	—	47	2	no	—
317	#336	—	47	2	no	—
318	C₄₇	C₄×#460	1	1	yes	characteristic, complemented, Sylow
319	C₂²×Q₈	—	47	1	no	—
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂×SD₁₆	—	47	8	no	—
325	C₂×SD₁₆	—	94	4	no	—
326	C₂×SD₁₆	—	94	4	no	—
327	C₂²×C₈	—	47	2	no	—
328	C₂²×C₈	—	47	2	no	—
329	#127	—	2	2	no	—
330	#127	C₄×D₄₇	1	4	yes	—
331	C₄×Q₈	—	47	4	no	—
332	C₄×Q₈	—	47	4	no	—
333	C₄×Q₈	—	94	2	no	—
334	C₄×Q₈	—	94	2	no	—
335	C₄×Q₈	—	94	2	no	—
336	C₄×Q₈	—	94	2	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	4	4	no	—
340	C₄×D₄	—	4	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	47	1	no	—
344	C₂×C₄⋊C₄	—	47	1	no	—
345	C₂×C₄⋊C₄	—	47	1	no	—
346	C₂×C₄⋊C₄	—	94	1	no	—
347	C₂×C₄⋊C₄	—	94	1	no	—
348	C₂×C₄⋊C₄	—	94	1	no	—
349	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₄²	—	94	1	no	—
354	C₂×C₄²	—	94	1	no	—
355	C₂×C₄²	—	94	1	no	—
356	C₂×C₄²	—	94	1	no	—
357	C₂×C₄²	—	94	1	no	—
358	C₂×C₄²	—	94	1	no	—
359	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	#106	—	94	4	no	—
367	C₄⋊C₈	—	47	4	no	—
368	C₄⋊C₈	—	94	2	no	—
369	#103	—	94	4	no	—
370	#102	—	47	8	no	—
371	#102	—	94	4	no	—
372	#102	—	94	4	no	—
373	C₄×C₈	—	94	4	no	—
374	#95	—	94	1	no	—
375	#95	—	94	1	no	—
376	#95	—	94	1	no	—
377	C₂⁴	—	2	2	no	—
378	C₂×Q₈	—	47	2	no	—
379	C₂×Q₈	—	47	2	no	—
380	C₂×Q₈	—	47	2	no	—
381	C₂×Q₈	—	94	1	no	—
382	C₂×Q₈	—	94	1	no	—
383	C₂×Q₈	—	94	1	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	4	no	—
399	C₂²×C₄	—	4	4	no	—
400	C₂²×C₄	—	94	1	no	—
401	C₂²×C₄	—	94	1	no	—
402	C₂²×C₄	—	94	1	no	—
403	C₂²×C₄	—	94	1	no	—
404	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	SD₁₆	—	94	16	no	—
412	C₂×C₈	—	47	4	no	—
413	C₂×C₈	—	94	2	no	—
414	C₂×C₈	—	94	2	no	—
415	C₂×C₈	—	94	2	no	—
416	C₂×C₈	—	94	2	no	—
417	C₂×C₈	—	94	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	47	2	no	—
423	C₄⋊C₄	—	47	2	no	—
424	C₄⋊C₄	—	47	2	no	—
425	C₄⋊C₄	—	94	4	no	—
426	C₄⋊C₄	—	94	4	no	—
427	C₄⋊C₄	—	94	4	no	—
428	C₄⋊C₄	—	94	1	no	—
429	C₄⋊C₄	—	94	1	no	—
430	C₄⋊C₄	—	94	1	no	—
431	C₂²⋊C₄	—	4	4	no	—
432	C₂²⋊C₄	—	4	4	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	4	1	no	—
439	C₄²	—	94	4	no	—
440	C₄²	—	94	4	no	—
441	C₄²	—	94	4	no	—
442	C₄²	—	188	2	no	—
443	C₄²	—	188	2	no	—
444	C₄²	—	188	2	no	—
445	C₄²	#10625335	1	4	yes	complemented
446	C₄²	C₂×C₄×D₄₇	1	2	yes	—
447	C₄²	#10625350	1	2	yes	—
448	C₄²	D₄×D₄₇	1	2	yes	—
449	C₄²	#10625352	1	2	yes	—
450	C₂³	—	2	4	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
458	Q₈	—	47	4	no	—
459	Q₈	—	94	2	no	—
460	Q₈	—	94	2	no	—
461	Q₈	—	94	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	8	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	8	no	—
481	C₂×C₄	—	94	2	no	—
482	C₂×C₄	—	94	2	no	—
483	C₂×C₄	—	94	2	no	—
484	C₂×C₄	—	94	2	no	—
485	C₂×C₄	—	94	2	no	—
486	C₂×C₄	—	94	2	no	—
487	C₂×C₄	—	188	1	no	—
488	C₂×C₄	—	188	1	no	—
489	C₂×C₄	—	188	1	no	—
490	C₂×C₄	—	188	1	no	—
491	C₂×C₄	—	188	1	no	—
492	C₂×C₄	—	188	1	no	—
493	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
494	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
495	C₂×C₄	#13093995	1	2	yes	—
496	C₂×C₄	#13093995	1	2	yes	—
497	C₂×C₄	C₂×#10625335	1	2	yes	—
498	C₂×C₄	C₂×#10625335	1	2	yes	—
499	C₂×C₄	C₂×#10625335	1	2	yes	—
500	C₂×C₄	#13094044	1	2	yes	—
501	C₂×C₄	#13094050	1	2	yes	—
502	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
504	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
505	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
507	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
508	C₈	—	94	4	no	—
509	C₈	—	188	2	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
518	C₂²	C₂×#13093995	1	1	yes	characteristic
519	C₂²	#15689630	1	1	yes	characteristic
520	C₂²	C₂²×#10625335	1	1	yes	characteristic
521	C₂²	C₂×#13094044	1	1	yes	characteristic
522	C₂²	C₂×#13094050	1	1	yes	characteristic
523	C₂²	#15689921	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	8	2	no	—
529	C₄	—	94	4	no	—
530	C₄	—	188	2	no	—
531	C₄	—	188	2	no	—
532	C₄	—	188	2	no	—
533	C₄	C₄×#10625335	1	4	yes	complemented
534	C₄	#15689320	1	4	yes	direct product factor
535	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
536	C₄	C₄×#10625352	1	1	yes	characteristic
537	C₄	#15689655	1	1	yes	characteristic
538	C₄	#15689670	1	1	yes	characteristic
539	C₂	—	8	4	no	—
540	C₂	C₄×#13093995	1	1	yes	characteristic
541	C₂	C₂×C₄×#10625335	1	1	yes	characteristic
542	C₂	C₄×#13094050	1	1	yes	characteristic
543	C₂	C₂×#15689320	1	1	yes	characteristic
544	C₂	#20252837	1	1	yes	characteristic
545	C₂	#20253415	1	1	yes	characteristic
546	C₂	#20253442	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#127	D₄₇
hypocenter	C₄₇	C₄×#460
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#127

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625335	C₂	semidirect
3. C₄²×Dic₉₄	C₂	semidirect
5. #20244149	C₂	semidirect
6. #20244012	C₂	semidirect
7. #20243746	C₂	semidirect
8. #20243390	C₂	semidirect
9. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
10. C₄×#13093945	C₂	semidirect
16. #15689320	C₄	direct (N × H)
48. C₂×#10625335	C₂×C₄	semidirect
55. C₄×Dic₉₄	C₂×C₄	semidirect
56. C₄×Dic₉₄	D₄	semidirect
71. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
75. #13093945	C₂×C₄	semidirect
149. C₄²×C₄₇	SD₁₆	semidirect
233. Dic₉₄	C₄×D₄	semidirect
256. C₄×C₄₇	C₄×SD₁₆	semidirect
257. C₄×C₄₇	#460	semidirect
318. C₄₇	C₄×#460	semidirect
445. C₄²	#10625335	semidirect
533. C₄	C₄×#10625335	semidirect
534. C₄	#15689320	direct (N × H)

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
C₄²×Dic₉₄	2
#20244316	2
#20244149	2
#20244012	2
#20243746	2
#20243390	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×#13093945	2
C₄×#127×C₄₇	2
C₄×#460	47

Subgroups — C4×#15689320 #26222470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689320 #26222470