Subgroups — C₄⋊C₄×C₄⋊Dic₄₇ #26137717

Order 12032.

1838 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×#15688993	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#20241622	C₂	1	4	yes	maximal
6	#20241618	C₂	1	2	yes	maximal
7	#20241617	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
15	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
16	#15688993	C₄	1	8	yes	complemented
17	C₄⋊C₄×Dic₄₇	—	2	8	no	—
18	C₄×C₄⋊Dic₄₇	—	2	8	no	—
19	C₄×C₄⋊Dic₄₇	C₄	1	8	yes	complemented
20	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
21	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
22	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
23	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₄	1	8	yes	complemented
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂³×Dic₄₇	C₂³	1	2	yes	—
31	C₂³×Dic₄₇	C₂³	1	4	yes	—
32	C₂³×Dic₄₇	C₂³	1	2	yes	—
33	C₂×C₄⋊Dic₄₇	—	2	4	no	—
34	C₂×C₄⋊Dic₄₇	—	2	4	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄⋊Dic₄₇	—	2	4	no	—
39	C₂×C₄⋊Dic₄₇	—	4	2	no	—
40	C₂×C₄⋊Dic₄₇	—	4	2	no	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
48	C₂×C₄×Dic₄₇	—	2	4	no	—
49	C₂×C₄×Dic₄₇	—	2	4	no	—
50	C₂×C₄×Dic₄₇	—	2	8	no	—
51	C₂×C₄×Dic₄₇	—	2	8	no	—
52	C₂×C₄×Dic₄₇	—	4	4	no	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
54	C₄₇⋊#95	—	2	8	no	—
55	C₄₇⋊#95	—	2	8	no	—
56	C₄₇⋊#95	—	4	4	no	—
57	C₄₇⋊#95	C₂×C₄	1	8	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
69	C₂×C₄²×C₄₇	—	2	4	no	—
70	C₂×C₄²×C₄₇	—	2	4	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
75	#95×C₄₇	C₂×C₄	1	8	yes	—
76	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	1	no	—
81	C₂²×C₄×C₄₇	—	2	1	no	—
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	2	yes	—
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	2	2	no	—
114	C₂²×Dic₄₇	—	2	2	no	—
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	2	2	no	—
117	C₂²×Dic₄₇	—	2	4	no	—
118	C₂²×Dic₄₇	—	2	4	no	—
119	C₂²×Dic₄₇	—	2	2	no	—
120	C₂²×Dic₄₇	—	2	2	no	—
121	C₂²×Dic₄₇	—	2	2	no	—
122	C₂²×Dic₄₇	—	2	4	no	—
123	C₂²×Dic₄₇	—	2	4	no	—
124	C₂²×Dic₄₇	—	2	2	no	—
125	C₂²×Dic₄₇	—	2	4	no	—
126	C₂²×Dic₄₇	—	2	4	no	—
127	C₂²×Dic₄₇	—	2	2	no	—
128	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
129	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
130	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
131	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
132	C₂²×Dic₄₇	C₂×Q₈	1	4	yes	—
133	C₄⋊C₄×C₄₇	—	2	8	no	—
134	C₄⋊C₄×C₄₇	C₄⋊C₄	1	16	yes	complemented
135	C₄²×C₄₇	—	2	16	no	—
136	C₄²×C₄₇	C₄²	1	16	yes	complemented
137	C₄⋊Dic₄₇	—	2	8	no	—
138	C₄⋊Dic₄₇	—	2	16	no	—
139	C₄⋊Dic₄₇	—	2	16	no	—
140	C₄⋊Dic₄₇	—	4	8	no	—
141	C₄⋊Dic₄₇	C₄⋊C₄	1	16	yes	direct product factor
142	C₄×Dic₄₇	—	2	16	no	—
143	C₄×Dic₄₇	—	4	16	no	—
144	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
180	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
181	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
183	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
184	C₂×C₄×C₄₇	#117	1	4	yes	—
185	C₂×C₄×C₄₇	#117	1	4	yes	—
186	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
190	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
191	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
192	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
193	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
194	C₂×Dic₄₇	—	2	4	no	—
195	C₂×Dic₄₇	—	2	4	no	—
196	C₂×Dic₄₇	—	2	4	no	—
197	C₂×Dic₄₇	—	2	4	no	—
198	C₂×Dic₄₇	—	2	4	no	—
199	C₂×Dic₄₇	—	2	4	no	—
200	C₂×Dic₄₇	—	2	4	no	—
201	C₂×Dic₄₇	—	2	4	no	—
202	C₂×Dic₄₇	—	2	8	no	—
203	C₂×Dic₄₇	—	2	8	no	—
204	C₂×Dic₄₇	—	2	8	no	—
205	C₂×Dic₄₇	—	2	4	no	—
206	C₂×Dic₄₇	—	4	4	no	—
207	C₂×Dic₄₇	—	4	2	no	—
208	C₂×Dic₄₇	—	4	4	no	—
209	C₂×Dic₄₇	—	4	2	no	—
210	C₂×Dic₄₇	—	4	4	no	—
211	C₂×Dic₄₇	—	4	2	no	—
212	C₂×Dic₄₇	—	4	2	no	—
213	C₂×Dic₄₇	—	4	4	no	—
214	C₂×Dic₄₇	C₂×C₄⋊C₄	1	8	yes	—
215	C₄⋊C₄²	—	47	1	no	maximal, Sylow
216	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
217	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
227	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₂²×C₄₇	#518	1	1	yes	characteristic
230	C₂²×C₄₇	#519	1	1	yes	characteristic
231	C₂²×C₄₇	#520	1	1	yes	characteristic
232	C₂²×C₄₇	#520	1	1	yes	characteristic
233	C₂²×C₄₇	#520	1	1	yes	characteristic
234	C₂²×C₄₇	#520	1	1	yes	characteristic
235	C₂²×C₄₇	D₄²	1	1	yes	characteristic
236	C₂²×C₄₇	#547	1	1	yes	characteristic
237	C₂²×C₄₇	#547	1	1	yes	characteristic
238	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
239	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
240	C₂²×C₄₇	#550	1	1	yes	characteristic
241	C₂²×C₄₇	#550	1	1	yes	characteristic
242	C₂²×C₄₇	#554	1	1	yes	characteristic
243	C₂²×C₄₇	#554	1	1	yes	characteristic
244	C₂²×C₄₇	#555	1	1	yes	characteristic
245	C₂²×C₄₇	#556	1	1	yes	characteristic
246	C₂²×C₄₇	#556	1	1	yes	characteristic
247	C₂²×C₄₇	#557	1	1	yes	characteristic
248	C₂²×C₄₇	#557	1	1	yes	characteristic
249	C₂²×C₄₇	Q₈²	1	1	yes	characteristic
250	C₂²×C₄₇	#559	1	1	yes	characteristic
251	C₄×C₄₇	—	2	8	no	—
252	C₄×C₄₇	—	2	4	no	—
253	C₄×C₄₇	—	4	4	no	—
254	C₄×C₄₇	C₄×C₄⋊C₄	1	8	yes	complemented
255	C₄×C₄₇	C₄×C₄⋊C₄	1	8	yes	complemented
256	Dic₄₇	—	2	8	no	—
257	Dic₄₇	—	4	4	no	—
258	Dic₄₇	—	4	8	no	—
259	C₂×#384	—	47	1	no	—
260	C₂×C₄×C₄⋊C₄	—	47	1	no	—
261	C₂×C₄×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄×C₄⋊C₄	—	47	2	no	—
263	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
264	#1436	—	47	4	no	—
265	C₄⋊#95	—	47	2	no	—
266	C₄⋊#95	—	47	2	no	—
267	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
268	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
269	C₂×C₄₇	#2274	1	1	yes	characteristic
270	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₄₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
273	C₂×C₄₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
274	C₂×C₄₇	#2354	1	1	yes	characteristic
275	C₂×C₄₇	#2354	1	1	yes	characteristic
276	C₂×C₄₇	#2355	1	1	yes	characteristic
277	C₂×C₄₇	#2355	1	1	yes	characteristic
278	C₂×C₄₇	#2365	1	1	yes	characteristic
279	C₂×C₄₇	#2365	1	1	yes	characteristic
280	C₂×C₄₇	#2366	1	1	yes	characteristic
281	C₂×C₄₇	#2369	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	—	47	1	no	—
283	C₂²×C₄⋊C₄	—	47	1	no	—
284	C₂²×C₄⋊C₄	—	47	2	no	—
285	C₂²×C₄⋊C₄	—	47	2	no	—
286	C₂²×C₄⋊C₄	—	47	2	no	—
287	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
289	C₂²×C₄²	—	47	2	no	—
290	C₂²×C₄²	—	47	4	no	—
291	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
292	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
293	#384	—	47	8	no	—
294	C₄×C₄⋊C₄	—	47	8	no	—
295	C₄×C₄⋊C₄	—	94	8	no	—
296	C₄×C₄⋊C₄	—	94	8	no	—
297	C₄×C₄⋊C₄	Dic₄₇	1	8	yes	complemented
298	C₂×#95	—	47	2	no	—
299	C₂×#95	—	47	4	no	—
300	C₂×#95	—	47	4	no	—
301	C₂×#95	—	47	4	no	—
302	C₂×#95	C₂×D₄₇	1	2	yes	—
303	C₄₇	C₄⋊C₄²	1	1	yes	characteristic, complemented, Sylow
304	C₂³×C₄	—	47	2	no	—
305	C₂³×C₄	—	47	4	no	—
306	C₂³×C₄	—	47	2	no	—
307	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
308	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
309	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
310	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	47	4	no	—
315	C₂×C₄⋊C₄	—	47	4	no	—
316	C₂×C₄⋊C₄	—	47	4	no	—
317	C₂×C₄⋊C₄	—	47	4	no	—
318	C₂×C₄⋊C₄	—	47	8	no	—
319	C₂×C₄⋊C₄	—	47	8	no	—
320	C₂×C₄⋊C₄	—	47	8	no	—
321	C₂×C₄⋊C₄	—	94	4	no	—
322	C₂×C₄⋊C₄	—	94	4	no	—
323	C₂×C₄⋊C₄	—	94	4	no	—
324	C₂×C₄⋊C₄	—	94	2	no	—
325	C₂×C₄⋊C₄	—	94	2	no	—
326	C₂×C₄⋊C₄	—	94	4	no	—
327	C₂×C₄⋊C₄	—	188	2	no	—
328	C₂×C₄⋊C₄	—	188	2	no	—
329	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
330	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
331	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
332	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	47	8	no	—
336	C₂×C₄²	—	94	4	no	—
337	C₂×C₄²	—	94	4	no	—
338	C₂×C₄²	—	94	8	no	—
339	C₂×C₄²	—	94	8	no	—
340	C₂×C₄²	—	188	4	no	—
341	C₂×C₄²	C₄×D₄₇	1	4	yes	—
342	C₂×C₄²	C₄×D₄₇	1	4	yes	—
343	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
344	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
345	#95	—	47	8	no	—
346	#95	—	94	8	no	—
347	#95	—	94	8	no	—
348	#95	—	188	4	no	—
349	#95	C₂×Dic₄₇	1	8	yes	—
350	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	47	4	no	—
366	C₂²×C₄	—	47	4	no	—
367	C₂²×C₄	—	47	4	no	—
368	C₂²×C₄	—	47	4	no	—
369	C₂²×C₄	—	47	8	no	—
370	C₂²×C₄	—	94	2	no	—
371	C₂²×C₄	—	94	2	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	94	2	no	—
374	C₂²×C₄	—	94	4	no	—
375	C₂²×C₄	—	94	2	no	—
376	C₂²×C₄	—	94	4	no	—
377	C₂²×C₄	—	94	2	no	—
378	C₂²×C₄	—	94	2	no	—
379	C₂²×C₄	—	94	4	no	—
380	C₂²×C₄	—	94	2	no	—
381	C₂²×C₄	—	94	4	no	—
382	C₂²×C₄	—	94	2	no	—
383	C₂²×C₄	—	94	4	no	—
384	C₂²×C₄	—	94	4	no	—
385	C₂²×C₄	—	94	2	no	—
386	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
387	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
388	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
389	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
390	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
391	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
392	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
393	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
394	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
395	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
396	C₂²×C₄	#10625350	1	2	yes	—
397	C₂²×C₄	#10625350	1	2	yes	—
398	C₂²×C₄	D₄×D₄₇	1	2	yes	—
399	C₂²×C₄	#10625352	1	2	yes	—
400	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
401	C₂²×C₄	#10625354	1	2	yes	—
402	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
403	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
404	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
405	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
406	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	47	16	no	—
409	C₄⋊C₄	—	94	8	no	—
410	C₄⋊C₄	—	94	16	no	—
411	C₄⋊C₄	—	94	16	no	—
412	C₄⋊C₄	—	188	8	no	—
413	C₄⋊C₄	C₄⋊Dic₄₇	1	16	yes	direct product factor
414	C₄²	—	2	16	no	—
415	C₄²	—	94	16	no	—
416	C₄²	—	188	16	no	—
417	C₄²	C₄×Dic₄₇	1	16	yes	complemented
418	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
419	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
420	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
421	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
422	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
423	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
424	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
425	C₂³	C₂×#10625352	1	1	yes	characteristic
426	C₂³	C₂×#10625350	1	1	yes	characteristic
427	C₂³	C₂×#10625350	1	1	yes	characteristic
428	C₂³	C₂×#10625354	1	1	yes	characteristic
429	C₂³	#13094070	1	1	yes	characteristic
430	C₂³	#13094070	1	1	yes	characteristic
431	C₂³	#13094071	1	1	yes	characteristic
432	C₂³	#13094071	1	1	yes	characteristic
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	47	8	no	—
453	C₂×C₄	—	94	4	no	—
454	C₂×C₄	—	94	4	no	—
455	C₂×C₄	—	94	4	no	—
456	C₂×C₄	—	94	4	no	—
457	C₂×C₄	—	94	4	no	—
458	C₂×C₄	—	94	4	no	—
459	C₂×C₄	—	94	4	no	—
460	C₂×C₄	—	94	8	no	—
461	C₂×C₄	—	94	4	no	—
462	C₂×C₄	—	94	8	no	—
463	C₂×C₄	—	94	8	no	—
464	C₂×C₄	—	94	4	no	—
465	C₂×C₄	—	188	4	no	—
466	C₂×C₄	—	188	2	no	—
467	C₂×C₄	—	188	4	no	—
468	C₂×C₄	—	188	2	no	—
469	C₂×C₄	—	188	4	no	—
470	C₂×C₄	—	188	2	no	—
471	C₂×C₄	—	188	2	no	—
472	C₂×C₄	—	188	4	no	—
473	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
474	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
475	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
476	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
477	C₂×C₄	C₂×C₄⋊Dic₄₇	1	8	yes	—
478	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
479	C₂×C₄	#13093982	1	4	yes	—
480	C₂×C₄	#13093983	1	4	yes	—
481	C₂×C₄	#13093986	1	4	yes	—
482	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
483	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
484	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
485	C₂×C₄	#13093989	1	4	yes	—
486	C₂×C₄	C₄×Dic₉₄	1	4	yes	—
487	C₂×C₄	C₄×Dic₉₄	1	4	yes	—
488	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
489	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
490	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
491	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
492	C₂²	C₂×#13093982	1	1	yes	characteristic
493	C₂²	C₂×#13093983	1	1	yes	characteristic
494	C₂²	C₂×#13093986	1	1	yes	characteristic
495	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
496	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
497	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
498	C₂²	C₂×#13093989	1	1	yes	characteristic
499	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
500	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
501	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
502	C₂²	#15689597	1	1	yes	characteristic
503	C₂²	#15689600	1	1	yes	characteristic
504	C₂²	#15689603	1	1	yes	characteristic
505	C₂²	#15689603	1	1	yes	characteristic
506	C₂²	#15689606	1	1	yes	characteristic
507	C₂²	#15689606	1	1	yes	characteristic
508	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
509	C₂²	#15689777	1	1	yes	characteristic
510	C₂²	#15689778	1	1	yes	characteristic
511	C₂²	D₄×Dic₉₄	1	1	yes	characteristic
512	C₂²	Q₈×D₁₈₈	1	1	yes	characteristic
513	C₂²	#15689794	1	1	yes	characteristic
514	C₂²	#15689795	1	1	yes	characteristic
515	C₂²	#15689830	1	1	yes	characteristic
516	C₂²	#15689833	1	1	yes	characteristic
517	C₂²	#15689838	1	1	yes	characteristic
518	C₂²	#15689843	1	1	yes	characteristic
519	C₂²	#15689846	1	1	yes	characteristic
520	C₂²	#15689851	1	1	yes	characteristic
521	C₂²	#15689852	1	1	yes	characteristic
522	C₂²	Q₈×Dic₉₄	1	1	yes	characteristic
523	C₂²	#15689858	1	1	yes	characteristic
524	C₄	—	2	8	no	—
525	C₄	—	2	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	94	8	no	—
528	C₄	—	188	4	no	—
529	C₄	—	188	8	no	—
530	C₄	C₄×C₄⋊Dic₄₇	1	8	yes	complemented
531	C₄	C₄⋊C₄×Dic₄₇	1	8	yes	complemented
532	C₂	C₂×C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
533	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
534	C₂	#20245744	1	1	yes	characteristic
535	C₂	D₄×C₄⋊Dic₄₇	1	1	yes	characteristic
536	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
537	C₂	C₄⋊C₄×Dic₉₄	1	1	yes	characteristic
538	C₂	Q₈×C₄⋊Dic₄₇	1	1	yes	characteristic
539	C₂	#20246335	1	1	yes	characteristic
540	C₂	#20246337	1	1	yes	characteristic
541	C₂	#20246343	1	1	yes	characteristic
542	C₂	#20246345	1	1	yes	characteristic
543	C₂	#20246444	1	1	yes	characteristic
544	C₂	#20246446	1	1	yes	characteristic
545	C₂	#20246452	1	1	yes	characteristic
546	C₂	#20246477	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. #15688993	C₄	semidirect
19. C₄×C₄⋊Dic₄₇	C₄	semidirect
28. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
134. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
136. C₄²×C₄₇	C₄²	semidirect
141. C₄⋊Dic₄₇	C₄⋊C₄	direct (N × H)
254. C₄×C₄₇	C₄×C₄⋊C₄	semidirect
255. C₄×C₄₇	C₄×C₄⋊C₄	semidirect
297. C₄×C₄⋊C₄	Dic₄₇	semidirect
303. C₄₇	C₄⋊C₄²	semidirect
413. C₄⋊C₄	C₄⋊Dic₄₇	direct (N × H)
417. C₄²	C₄×Dic₄₇	semidirect
530. C₄	C₄×C₄⋊Dic₄₇	semidirect
531. C₄	C₄⋊C₄×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688993	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
#20241622	2
#20241618	2
#20241617	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄⋊C₄²	47

Subgroups — C4⋊C4×C4⋊Dic47 #26137717

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×C₄⋊Dic₄₇ #26137717