Subgroups — C₄×#15688983 #26137500

Order 12032.

2782 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688983	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
4	#20241618	C₂	1	2	yes	maximal, complemented
5	#20241615	C₂	1	2	yes	maximal, complemented
6	#20241611	C₂	1	2	yes	maximal
7	C₄×C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
10	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
12	#15688983	C₄	1	16	yes	direct product factor
13	C₄×C₄⋊Dic₄₇	—	2	8	no	—
14	C₄×C₂²⋊Dic₄₇	—	2	8	no	—
15	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
16	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
17	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
18	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
19	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	—	2	8	no	—
23	C₂²×C₄²×C₄₇	C₄	1	8	yes	complemented
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₂³×Dic₄₇	C₂³	1	8	yes	—
29	C₂×C₄⋊Dic₄₇	—	2	8	no	—
30	C₂×C₄⋊Dic₄₇	—	2	8	no	—
31	C₂×C₄⋊Dic₄₇	C₂×C₄	1	16	yes	complemented
32	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
33	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
34	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	16	yes	—
35	C₂×C₄×Dic₄₇	—	2	8	no	—
36	C₂×C₄×Dic₄₇	—	2	8	no	—
37	C₂×C₄×Dic₄₇	—	2	8	no	—
38	C₄₇⋊#95	—	2	8	no	—
39	C₄₇⋊#95	—	2	8	no	—
40	C₄₇⋊#95	—	2	8	no	—
41	C₄₇⋊#95	C₂×C₄	1	16	yes	complemented
42	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	—	2	4	no	—
44	C₂³×C₄×C₄₇	—	2	4	no	—
45	C₂³×C₄×C₄₇	—	2	4	no	—
46	C₂³×C₄×C₄₇	—	2	4	no	—
47	C₂³×C₄×C₄₇	—	2	4	no	—
48	C₂³×C₄×C₄₇	—	2	4	no	—
49	C₂³×C₄×C₄₇	—	2	4	no	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
53	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂³×C₄×C₄₇	D₄	1	4	yes	—
55	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	—	2	4	no	—
64	C₂×C₄²×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	—	2	32	no	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	D₄	1	8	yes	—
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	—	2	2	no	—
73	C₂⁴×C₄₇	—	2	2	no	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
78	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
79	C₂⁴×C₄₇	#41	1	4	yes	—
80	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	32	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	2	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	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	8	no	—
93	C₂²×C₄×C₄₇	—	2	8	no	—
94	C₂²×C₄×C₄₇	—	2	8	no	—
95	C₂²×C₄×C₄₇	—	2	8	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	32	no	—
98	C₂²×C₄×C₄₇	—	2	16	no	—
99	C₂²×C₄×C₄₇	—	2	16	no	—
100	C₂²×C₄×C₄₇	C₄²	1	16	yes	complemented
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	complemented
102	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₄₇	#41	1	4	yes	—
118	C₂²×C₄×C₄₇	#41	1	4	yes	—
119	C₂²×C₄×C₄₇	#41	1	4	yes	—
120	C₂²×Dic₄₇	—	2	8	no	—
121	C₂²×Dic₄₇	—	2	8	no	—
122	C₂²×Dic₄₇	—	2	8	no	—
123	C₂²×Dic₄₇	—	2	8	no	—
124	C₂²×Dic₄₇	—	2	8	no	—
125	C₂²×Dic₄₇	—	2	8	no	—
126	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
127	C₄²×C₄₇	—	2	8	no	—
128	C₄²×C₄₇	—	2	8	no	—
129	C₄²×C₄₇	—	2	8	no	—
130	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	complemented
131	C₂²⋊Dic₄₇	—	2	32	no	—
132	C₄⋊Dic₄₇	—	2	32	no	—
133	C₄×Dic₄₇	—	4	16	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	2	8	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	8	no	—
143	C₂³×C₄₇	—	2	8	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
148	C₂³×C₄₇	#117	1	4	yes	—
149	C₂³×C₄₇	C₄×D₄	1	8	yes	—
150	C₂³×C₄₇	C₄×Q₈	1	8	yes	—
151	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
152	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂³×C₄₇	C₂×#41	1	2	yes	—
157	C₂³×C₄₇	C₂×#41	1	2	yes	—
158	C₂³×C₄₇	C₂×#41	1	2	yes	—
159	C₂³×C₄₇	C₂×#41	1	2	yes	—
160	C₂×C₄×C₄₇	—	2	32	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	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	8	no	—
173	C₂×C₄×C₄₇	—	2	8	no	—
174	C₂×C₄×C₄₇	—	2	32	no	—
175	C₂×C₄×C₄₇	—	2	32	no	—
176	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
177	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
183	C₂×C₄×C₄₇	#117	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	16	yes	—
187	C₂×C₄×C₄₇	#121	1	8	yes	—
188	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
189	C₂×Dic₄₇	—	2	16	no	—
190	C₂×Dic₄₇	—	2	16	no	—
191	C₂×Dic₄₇	—	2	16	no	—
192	C₂×Dic₄₇	—	4	8	no	—
193	C₂×Dic₄₇	—	4	8	no	—
194	C₂×Dic₄₇	—	4	8	no	—
195	C₂×Dic₄₇	—	4	8	no	—
196	C₄×#380	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	4	no	—
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	16	no	—
204	C₂²×C₄₇	—	2	16	no	—
205	C₂²×C₄₇	C₄×C₄⋊C₄	1	8	yes	complemented
206	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
207	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
214	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
215	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
216	C₂²×C₄₇	C₄×#41	1	4	yes	—
217	C₂²×C₄₇	C₂×#121	1	2	yes	—
218	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
219	C₂²×C₄₇	#525	1	4	yes	—
220	C₂²×C₄₇	#529	1	4	yes	—
221	C₂²×C₄₇	#532	1	2	yes	—
222	C₂²×C₄₇	#533	1	2	yes	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	2	4	no	—
225	C₄×C₄₇	—	2	4	no	—
226	C₄×C₄₇	—	2	4	no	—
227	C₄×C₄₇	C₄×C₂²⋊C₄	1	8	yes	complemented
228	C₄×C₄₇	#380	1	8	yes	complemented
229	Dic₄₇	—	4	16	no	—
230	C₂³×C₄²	D₄₇	1	1	yes	characteristic
231	C₂×#380	—	47	2	no	—
232	C₂×C₄×C₄⋊C₄	—	47	2	no	—
233	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
234	C₄⋊#95	—	47	2	no	—
235	#1434	—	47	2	no	—
236	C₂²⋊#95	—	47	2	no	—
237	C₄×#95	—	47	2	no	—
238	C₂×C₄₇	—	2	8	no	—
239	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
243	C₂×C₄₇	#2280	1	1	yes	characteristic
244	C₂×C₄₇	#2283	1	1	yes	characteristic
245	C₂×C₄₇	#2285	1	1	yes	characteristic
246	C₂×C₄₇	C₄×#121	1	4	yes	—
247	C₂×C₄₇	C₄×C₂²⋊Q₈	1	4	yes	—
248	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
249	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
250	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	—	47	4	no	—
252	C₂²×C₂²⋊C₄	—	47	4	no	—
253	C₂²×C₄²	—	2	8	no	—
254	C₂²×C₄²	—	47	4	no	—
255	C₂²×C₄²	Dic₄₇	1	8	yes	complemented
256	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
257	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
258	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
259	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
260	#380	—	47	16	no	—
261	C₄×C₄⋊C₄	—	94	8	no	—
262	C₄×C₂²⋊C₄	—	94	8	no	—
263	C₂×#95	—	47	4	no	—
264	C₂×#95	—	47	4	no	—
265	C₂×#95	—	47	4	no	—
266	C₂×#95	—	47	4	no	—
267	C₄₇	C₄×#380	1	1	yes	characteristic, complemented, Sylow
268	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	4	no	—
273	C₂³×C₄	—	2	4	no	—
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	47	8	no	—
277	C₂³×C₄	Dic₉₄	1	4	yes	—
278	C₂³×C₄	C₄×D₄₇	1	8	yes	—
279	C₂³×C₄	D₁₈₈	1	4	yes	—
280	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
281	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
282	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
283	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
287	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	47	16	no	—
290	C₂×C₄⋊C₄	—	94	8	no	—
291	C₂×C₄⋊C₄	—	94	8	no	—
292	C₂×C₂²⋊C₄	—	47	16	no	—
293	C₂×C₂²⋊C₄	—	94	8	no	—
294	C₂×C₂²⋊C₄	—	94	8	no	—
295	C₂×C₄²	—	2	4	no	—
296	C₂×C₄²	—	2	4	no	—
297	C₂×C₄²	—	2	4	no	—
298	C₂×C₄²	—	2	32	no	—
299	C₂×C₄²	—	94	8	no	—
300	C₂×C₄²	—	94	8	no	—
301	C₂×C₄²	—	94	8	no	—
302	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
303	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
304	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
305	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
306	C₂×C₄²	C₂²⋊D₄₇	1	8	yes	—
307	#95	—	47	16	no	—
308	#95	—	94	8	no	—
309	#95	—	94	8	no	—
310	#95	—	94	8	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×Dic₉₄	1	2	yes	—
316	C₂⁴	C₂×C₄×D₄₇	1	4	yes	—
317	C₂⁴	C₂×D₁₈₈	1	2	yes	—
318	C₂⁴	#10625350	1	4	yes	—
319	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
320	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	—	2	32	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	2	32	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	47	16	no	—
341	C₂²×C₄	—	94	8	no	—
342	C₂²×C₄	—	94	8	no	—
343	C₂²×C₄	—	94	8	no	—
344	C₂²×C₄	—	94	8	no	—
345	C₂²×C₄	—	94	8	no	—
346	C₂²×C₄	—	94	8	no	—
347	C₂²×C₄	C₄×Dic₄₇	1	16	yes	complemented
348	C₂²×C₄	C₄⋊Dic₄₇	1	16	yes	complemented
349	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
350	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
351	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
352	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
353	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
354	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
355	C₂²×C₄	#10625350	1	4	yes	—
356	C₂²×C₄	#10625350	1	4	yes	—
357	C₂²×C₄	#10625350	1	4	yes	—
358	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
359	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
360	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
361	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
362	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
363	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
364	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
365	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
366	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
367	C₄⋊C₄	—	94	32	no	—
368	C₂²⋊C₄	—	94	32	no	—
369	C₄²	—	2	8	no	—
370	C₄²	—	2	8	no	—
371	C₄²	—	2	8	no	—
372	C₄²	—	188	16	no	—
373	C₄²	C₂²⋊Dic₄₇	1	16	yes	complemented
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
387	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
388	C₂³	#13093983	1	4	yes	—
389	C₂³	C₄×D₁₈₈	1	8	yes	—
390	C₂³	C₄×Dic₉₄	1	8	yes	—
391	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
392	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
393	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
394	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
395	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
396	C₂³	C₂×#10625350	1	2	yes	—
397	C₂³	C₂×#10625350	1	2	yes	—
398	C₂³	C₂×#10625350	1	2	yes	—
399	C₂³	C₂×#10625350	1	2	yes	—
400	C₂×C₄	—	2	32	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	32	no	—
415	C₂×C₄	—	2	32	no	—
416	C₂×C₄	—	94	16	no	—
417	C₂×C₄	—	94	16	no	—
418	C₂×C₄	—	94	16	no	—
419	C₂×C₄	—	188	8	no	—
420	C₂×C₄	—	188	8	no	—
421	C₂×C₄	—	188	8	no	—
422	C₂×C₄	—	188	8	no	—
423	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
424	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
425	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
426	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
427	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
428	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
429	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
430	C₂×C₄	#13093983	1	4	yes	—
431	C₂×C₄	#13093983	1	4	yes	—
432	C₂×C₄	#13093983	1	4	yes	—
433	C₂×C₄	C₄×C₂²⋊D₄₇	1	16	yes	—
434	C₂×C₄	#13093998	1	8	yes	—
435	C₂×C₄	#13094003	1	8	yes	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	16	no	—
441	C₂²	—	2	16	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	C₄×C₄⋊Dic₄₇	1	8	yes	complemented
445	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
446	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
447	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
448	C₂²	C₂×#13093983	1	1	yes	characteristic
449	C₂²	C₂×#13093983	1	1	yes	characteristic
450	C₂²	C₂×#13093983	1	1	yes	characteristic
451	C₂²	C₂×#13093983	1	1	yes	characteristic
452	C₂²	C₂×C₄×C₂²⋊D₄₇	1	4	yes	—
453	C₂²	C₂×C₄×D₁₈₈	1	2	yes	—
454	C₂²	C₂×C₄×Dic₉₄	1	2	yes	—
455	C₂²	C₄×#10625350	1	4	yes	—
456	C₂²	C₂×#13093998	1	2	yes	—
457	C₂²	C₂×#13094003	1	2	yes	—
458	C₂²	#15689634	1	4	yes	—
459	C₂²	#15689657	1	4	yes	—
460	C₂²	#15689673	1	2	yes	—
461	C₂²	#15689680	1	2	yes	—
462	C₄	—	2	4	no	—
463	C₄	—	2	4	no	—
464	C₄	—	2	4	no	—
465	C₄	—	2	4	no	—
466	C₄	—	188	16	no	—
467	C₄	C₄×C₂²⋊Dic₄₇	1	8	yes	complemented
468	C₄	#15688983	1	8	yes	direct product factor
469	C₂	—	2	8	no	—
470	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₂	C₂×C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
472	C₂	C₄×#13093983	1	1	yes	characteristic
473	C₂	C₂×#15688983	1	1	yes	characteristic
474	C₂	#20245771	1	1	yes	characteristic
475	C₂	#20245786	1	1	yes	characteristic
476	C₂	#20245795	1	1	yes	characteristic
477	C₂	C₄×#13093998	1	4	yes	—
478	C₂	C₄×#13094003	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle, cosocle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₄×#380
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
4. #20241618	C₂	semidirect
5. #20241615	C₂	semidirect
7. C₄×C₄₇⋊#95	C₂	semidirect
12. #15688983	C₄	direct (N × H)
23. C₂²×C₄²×C₄₇	C₄	semidirect
31. C₂×C₄⋊Dic₄₇	C₂×C₄	semidirect
41. C₄₇⋊#95	C₂×C₄	semidirect
100. C₂²×C₄×C₄₇	C₄²	semidirect
101. C₂²×C₄×C₄₇	C₄⋊C₄	semidirect
130. C₄²×C₄₇	C₂²⋊C₄	semidirect
205. C₂²×C₄₇	C₄×C₄⋊C₄	semidirect
227. C₄×C₄₇	C₄×C₂²⋊C₄	semidirect
228. C₄×C₄₇	#380	semidirect
255. C₂²×C₄²	Dic₄₇	semidirect
267. C₄₇	C₄×#380	semidirect
347. C₂²×C₄	C₄×Dic₄₇	semidirect
348. C₂²×C₄	C₄⋊Dic₄₇	semidirect
373. C₄²	C₂²⋊Dic₄₇	semidirect
444. C₂²	C₄×C₄⋊Dic₄₇	semidirect
467. C₄	C₄×C₂²⋊Dic₄₇	semidirect
468. C₄	#15688983	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×#15688983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
#20241618	2
#20241615	2
#20241611	2
C₄×C₄₇⋊#95	2
C₂³×C₄²×C₄₇	2
C₄×#380	47

Subgroups — C4×#15688983 #26137500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15688983 #26137500