Subgroups — D₄×#13093948 #26231710

Order 12032.

1530 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093948	C₂	1	2	yes	maximal, complemented
3	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244312	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244191	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243812	C₂	1	2	yes	maximal, complemented
7	#20243696	C₂	1	2	yes	maximal, complemented
8	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243323	C₂	1	2	yes	maximal, complemented
10	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	—	2	1	no	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	D₄×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13093948	—	2	8	no	—
18	C₂×#13093948	C₂²	1	1	yes	characteristic
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093948	C₂²	1	2	yes	—
22	C₂×#13093948	C₂²	1	2	yes	—
23	C₂×#13093948	C₂²	1	2	yes	—
24	C₂×#13093948	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15689022	—	2	1	no	—
28	#15688998	—	2	2	no	—
29	#15688993	C₂²	1	1	yes	characteristic
30	#15688983	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	1	yes	characteristic
34	#15688885	C₂²	1	2	yes	—
35	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
36	D₄×Q₈×C₄₇	—	2	4	no	—
37	D₄×Q₈×C₄₇	C₄	1	8	yes	complemented
38	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
39	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
41	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₄₇	—	2	1	no	—
44	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
45	C₂³×Dic₄₇	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	—	2	4	no	—
47	C₂²×C₄₇⋊C₈	—	2	4	no	—
48	C₂²×C₄₇⋊C₈	—	4	2	no	—
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	D₄×Dic₄₇	—	4	4	no	—
53	C₂×C₄⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	4	2	no	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	#13093948	—	2	4	no	—
65	#13093948	—	2	2	no	—
66	#13093948	—	2	4	no	—
67	#13093948	—	2	4	no	—
68	#13093948	—	4	2	no	—
69	#13093948	—	4	2	no	—
70	#13093948	D₄	1	4	yes	direct product factor
71	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
72	C₄×C₄₇⋊C₈	—	2	2	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₂²×Q₈×C₄₇	—	2	2	no	—
76	C₂²×Q₈×C₄₇	—	2	4	no	—
77	C₂²×Q₈×C₄₇	—	2	4	no	—
78	C₂²×Q₈×C₄₇	—	2	4	no	—
79	C₂²×Q₈×C₄₇	—	4	2	no	—
80	C₂²×Q₈×C₄₇	—	4	2	no	—
81	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
83	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	—	2	2	no	—
86	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₄₇	—	2	8	no	—
88	C₄⋊Q₈×C₄₇	—	2	2	no	—
89	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
90	C₂²⋊Q₈×C₄₇	—	2	4	no	—
91	C₂²⋊Q₈×C₄₇	—	2	16	no	—
92	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
93	C₄×Q₈×C₄₇	—	2	2	no	—
94	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₄×D₄×C₄₇	—	2	8	no	—
96	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
97	C₄×D₄×C₄₇	D₄	1	4	yes	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
106	C₂×C₄²×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₄₇	—	2	8	no	—
110	C₂×Q₈×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	2	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×Q₈×C₄₇	—	2	1	no	—
114	C₂×Q₈×C₄₇	—	2	16	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	4	4	no	—
120	C₂×Q₈×C₄₇	—	4	4	no	—
121	C₂×Q₈×C₄₇	—	4	8	no	—
122	C₂×Q₈×C₄₇	—	4	8	no	—
123	C₂×Q₈×C₄₇	—	4	8	no	—
124	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×Q₈×C₄₇	#41	1	2	yes	—
128	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
129	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
130	C₂×D₄×C₄₇	Q₁₆	1	4	yes	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	8	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	4	4	no	—
140	C₂²×C₄×C₄₇	—	4	4	no	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²×Dic₄₇	—	2	1	no	—
148	C₂²×Dic₄₇	—	2	1	no	—
149	C₂²×Dic₄₇	—	2	2	no	—
150	C₂²×Dic₄₇	—	4	4	no	—
151	C₂²×Dic₄₇	—	4	4	no	—
152	C₂²×Dic₄₇	—	8	2	no	—
153	C₄⋊C₄×C₄₇	—	2	4	no	—
154	C₄⋊C₄×C₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	2	4	no	—
156	C₄⋊C₄×C₄₇	—	2	8	no	—
157	C₄⋊C₄×C₄₇	—	2	1	no	—
158	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
159	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂²⋊C₄×C₄₇	—	2	8	no	—
161	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
162	C₄²×C₄₇	—	2	4	no	—
163	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
164	C₄²×C₄₇	C₂×D₄	1	2	yes	—
165	C₂²⋊Dic₄₇	—	4	4	no	—
166	C₄⋊Dic₄₇	—	2	1	no	—
167	C₄⋊Dic₄₇	—	2	2	no	—
168	C₄⋊Dic₄₇	—	2	1	no	—
169	C₄⋊Dic₄₇	—	2	1	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	4	4	no	—
172	C₄⋊Dic₄₇	—	4	2	no	—
173	C₄⋊Dic₄₇	—	8	1	no	—
174	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
175	C₄×Dic₄₇	—	4	2	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	1	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	2	no	—
184	C₂×C₄₇⋊C₈	—	4	8	no	—
185	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
186	C₂³×C₄₇	—	2	2	no	—
187	C₂³×C₄₇	—	2	2	no	—
188	C₂³×C₄₇	—	2	2	no	—
189	C₂³×C₄₇	—	2	2	no	—
190	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
191	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
192	C₂³×C₄₇	C₂×Q₁₆	1	4	yes	—
193	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₄₇	—	2	2	no	—
195	Q₈×C₄₇	—	2	2	no	—
196	Q₈×C₄₇	—	2	2	no	—
197	Q₈×C₄₇	—	2	4	no	—
198	Q₈×C₄₇	—	2	4	no	—
199	Q₈×C₄₇	—	4	16	no	—
200	Q₈×C₄₇	—	4	2	no	—
201	Q₈×C₄₇	—	4	2	no	—
202	Q₈×C₄₇	C₄×D₄	1	4	yes	complemented
203	D₄×C₄₇	#103	1	16	yes	complemented
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	4	no	—
217	C₂×C₄×C₄₇	—	4	16	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	1	no	—
221	C₂×C₄×C₄₇	—	4	1	no	—
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
224	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
226	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
227	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×Dic₄₇	—	2	2	no	—
234	C₂×Dic₄₇	—	4	1	no	—
235	C₂×Dic₄₇	—	4	1	no	—
236	C₂×Dic₄₇	—	4	2	no	—
237	C₂×Dic₄₇	—	4	1	no	—
238	C₂×Dic₄₇	—	4	1	no	—
239	C₂×Dic₄₇	—	4	2	no	—
240	C₂×Dic₄₇	—	4	2	no	—
241	C₂×Dic₄₇	—	4	1	no	—
242	C₂×Dic₄₇	—	8	8	no	—
243	C₄₇⋊C₈	—	2	2	no	—
244	C₄₇⋊C₈	—	4	2	no	—
245	C₄₇⋊C₈	—	4	1	no	—
246	D₄×#103	—	47	1	no	maximal, Sylow
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	2	4	no	—
249	C₂²×C₄₇	—	2	4	no	—
250	C₂²×C₄₇	—	2	4	no	—
251	C₂²×C₄₇	—	2	4	no	—
252	C₂²×C₄₇	—	2	4	no	—
253	C₂²×C₄₇	C₂×#103	1	8	yes	complemented
254	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄₇	D₄²	1	1	yes	characteristic
256	C₂²×C₄₇	#546	1	1	yes	characteristic
257	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
258	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
259	C₂²×C₄₇	#577	1	1	yes	characteristic
260	C₂²×C₄₇	#578	1	1	yes	characteristic
261	C₄×C₄₇	—	2	4	no	—
262	C₄×C₄₇	—	2	4	no	—
263	C₄×C₄₇	—	2	2	no	—
264	C₄×C₄₇	—	4	4	no	—
265	C₄×C₄₇	—	4	2	no	—
266	C₄×C₄₇	C₂×#103	1	4	yes	complemented
267	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₄₇	#518	1	1	yes	characteristic
269	C₄×C₄₇	D₄²	1	1	yes	characteristic
270	C₄×C₄₇	#546	1	1	yes	characteristic
271	Dic₄₇	—	4	2	no	—
272	Dic₄₇	—	8	2	no	—
273	Dic₄₇	—	8	1	no	—
274	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic
275	C₂×C₈×D₄	—	47	1	no	—
276	C₂²×#103	—	47	2	no	—
277	D₄×C₄⋊C₄	—	47	1	no	—
278	#1981	—	47	1	no	—
279	#1956	—	47	1	no	—
280	#1892	—	47	2	no	—
281	#1872	—	47	2	no	—
282	#1803	—	47	1	no	—
283	#1787	—	47	2	no	—
284	C₄×#103	—	47	1	no	—
285	C₂×C₄₇	—	2	8	no	—
286	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
288	C₂×C₄₇	#2898	1	1	yes	characteristic
289	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
290	C₂×C₄₇	D₄×Q₁₆	1	1	yes	characteristic
291	C₂×C₄₇	#3298	1	1	yes	characteristic
292	C₂×C₄₇	#3299	1	1	yes	characteristic
293	C₂³×Q₈	C₂×D₄₇	1	2	yes	—
294	C₂³×C₈	—	47	2	no	—
295	D₄×Q₈	—	2	4	no	—
296	D₄×Q₈	Dic₄₇	1	8	yes	complemented
297	C₂×C₄⋊Q₈	—	2	1	no	—
298	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
299	C₂×C₂²⋊Q₈	—	2	2	no	—
300	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
301	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	94	1	no	—
304	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	—	47	2	no	—
306	C₈×D₄	—	94	4	no	—
307	C₂×C₄⋊C₈	—	47	1	no	—
308	C₂×#103	—	47	1	no	—
309	C₂×#103	—	47	2	no	—
310	C₂×#103	—	47	2	no	—
311	C₂×#103	—	47	2	no	—
312	C₂×#103	—	47	1	no	—
313	C₂×#103	—	47	2	no	—
314	C₂×#103	—	47	2	no	—
315	C₂×#103	—	94	8	no	—
316	C₂×C₂²⋊C₈	—	47	2	no	—
317	C₂×C₄×C₈	—	47	1	no	—
318	#389	—	94	1	no	—
319	#385	—	94	2	no	—
320	#384	—	47	1	no	—
321	#380	—	47	2	no	—
322	C₄×C₄⋊C₄	—	47	1	no	—
323	#340	—	47	2	no	—
324	#340	—	47	1	no	—
325	#340	—	47	1	no	—
326	C₄₇	D₄×#103	1	1	yes	characteristic, complemented, Sylow
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	—	2	4	no	—
329	C₂²×Q₈	—	2	4	no	—
330	C₂²×Q₈	—	2	4	no	—
331	C₂²×Q₈	—	4	2	no	—
332	C₂²×Q₈	—	4	2	no	—
333	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	complemented
334	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
335	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
337	C₂³×C₄	—	2	2	no	—
338	C₂³×C₄	—	94	2	no	—
339	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
340	C₂²×C₈	—	47	1	no	—
341	C₂²×C₈	—	47	2	no	—
342	C₂²×C₈	—	47	1	no	—
343	C₂²×C₈	—	94	4	no	—
344	C₂²×C₈	—	94	4	no	—
345	C₂²×C₈	—	188	2	no	—
346	C₄⋊Q₈	—	2	8	no	—
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	16	no	—
351	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	—	188	4	no	—
356	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
357	C₄×D₄	C₂²⋊D₄₇	1	4	yes	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	47	1	no	—
363	C₂×C₄⋊C₄	—	47	2	no	—
364	C₂×C₄⋊C₄	—	47	1	no	—
365	C₂×C₄⋊C₄	—	94	4	no	—
366	C₂×C₄⋊C₄	—	94	1	no	—
367	C₂×C₄⋊C₄	—	94	2	no	—
368	C₂×C₄⋊C₄	—	94	1	no	—
369	C₂×C₄⋊C₄	—	188	2	no	—
370	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	94	2	no	—
374	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	94	1	no	—
377	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
378	C₄⋊C₈	—	94	2	no	—
379	#103	—	47	4	no	—
380	#103	—	94	4	no	—
381	#103	—	94	4	no	—
382	#103	—	94	4	no	—
383	#103	—	94	2	no	—
384	#103	—	188	2	no	—
385	#103	—	188	2	no	—
386	C₂²⋊C₈	—	94	4	no	—
387	C₄×C₈	—	94	2	no	—
388	#95	—	94	1	no	—
389	#95	—	94	2	no	—
390	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	16	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×Q₈	—	4	4	no	—
403	C₂×Q₈	—	4	8	no	—
404	C₂×Q₈	—	4	8	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	D₄×D₄₇	1	2	yes	—
407	C₂×Q₈	#10625352	1	2	yes	—
408	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
409	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
410	C₂×D₄	#10625336	1	4	yes	—
411	C₂×D₄	#10625337	1	4	yes	—
412	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	—	94	1	no	—
424	C₂²×C₄	—	94	1	no	—
425	C₂²×C₄	—	94	2	no	—
426	C₂²×C₄	—	376	2	no	—
427	C₂²×C₄	—	188	4	no	—
428	C₂²×C₄	—	188	4	no	—
429	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
430	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
432	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
433	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
434	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
435	C₂×C₈	—	47	2	no	—
436	C₂×C₈	—	94	1	no	—
437	C₂×C₈	—	94	1	no	—
438	C₂×C₈	—	94	2	no	—
439	C₂×C₈	—	94	1	no	—
440	C₂×C₈	—	94	2	no	—
441	C₂×C₈	—	94	1	no	—
442	C₂×C₈	—	94	1	no	—
443	C₂×C₈	—	94	2	no	—
444	C₂×C₈	—	188	8	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	47	2	no	—
451	C₄⋊C₄	—	94	1	no	—
452	C₄⋊C₄	—	94	2	no	—
453	C₄⋊C₄	—	94	1	no	—
454	C₄⋊C₄	—	94	1	no	—
455	C₄⋊C₄	—	94	2	no	—
456	C₄⋊C₄	—	376	1	no	—
457	C₄⋊C₄	—	188	4	no	—
458	C₄⋊C₄	—	188	2	no	—
459	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
460	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₂²⋊C₄	—	188	4	no	—
463	C₂²⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
464	C₄²	—	2	4	no	—
465	C₄²	—	188	2	no	—
466	C₄²	C₂²×Dic₄₇	1	2	yes	—
467	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
473	C₂³	C₂×#10625336	1	4	yes	—
474	C₂³	C₂×#10625337	1	4	yes	—
475	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
476	Q₈	—	2	2	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	4	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	4	16	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	D₄×Dic₄₇	1	4	yes	complemented
485	D₄	#13093948	1	16	yes	direct product factor
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	4	16	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	94	2	no	—
505	C₂×C₄	—	376	8	no	—
506	C₂×C₄	—	188	2	no	—
507	C₂×C₄	—	188	1	no	—
508	C₂×C₄	—	188	1	no	—
509	C₂×C₄	—	188	2	no	—
510	C₂×C₄	—	188	2	no	—
511	C₂×C₄	—	188	1	no	—
512	C₂×C₄	—	188	1	no	—
513	C₂×C₄	—	188	1	no	—
514	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
515	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
516	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
517	C₂×C₄	C₂×#10625336	1	2	yes	—
518	C₂×C₄	C₂×#10625337	1	2	yes	—
519	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
521	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
522	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
523	C₂×C₄	#13094069	1	1	yes	characteristic
524	C₂×C₄	#13094069	1	1	yes	characteristic
525	C₈	—	94	2	no	—
526	C₈	—	188	2	no	—
527	C₈	—	188	1	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	C₂×#13093948	1	8	yes	complemented
535	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
536	C₂²	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
537	C₂²	#15689767	1	1	yes	characteristic
538	C₂²	C₂²×#10625336	1	1	yes	characteristic
539	C₂²	C₂²×#10625337	1	1	yes	characteristic
540	C₂²	#15689931	1	1	yes	characteristic
541	C₂²	#15689938	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	376	1	no	—
548	C₄	—	376	2	no	—
549	C₄	—	188	2	no	—
550	C₄	C₂×#13093948	1	4	yes	complemented
551	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
552	C₄	#15689598	1	1	yes	characteristic
553	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
554	C₄	#15689767	1	1	yes	characteristic
555	C₂	—	2	8	no	—
556	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
557	C₂	C₂²×#13093948	1	1	yes	characteristic
558	C₂	#20251921	1	1	yes	characteristic
559	C₂	D₄×#10625336	1	1	yes	characteristic
560	C₂	D₄×#10625337	1	1	yes	characteristic
561	C₂	#20255253	1	1	yes	characteristic
562	C₂	#20255264	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	D₄×#103
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093948	C₂	semidirect
4. #20244312	C₂	semidirect
5. #20244191	C₂	semidirect
6. #20243812	C₂	semidirect
7. #20243696	C₂	semidirect
8. #20243393	C₂	semidirect
9. #20243323	C₂	semidirect
10. C₄×#13093948	C₂	semidirect
37. D₄×Q₈×C₄₇	C₄	semidirect
70. #13093948	D₄	direct (N × H)
81. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
89. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
92. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
94. C₄×Q₈×C₄₇	C₂×C₄	semidirect
202. Q₈×C₄₇	C₄×D₄	semidirect
203. D₄×C₄₇	#103	semidirect
253. C₂²×C₄₇	C₂×#103	semidirect
266. C₄×C₄₇	C₂×#103	semidirect
296. D₄×Q₈	Dic₄₇	semidirect
326. C₄₇	D₄×#103	semidirect
333. C₂²×Q₈	C₂×Dic₄₇	semidirect
348. C₄⋊Q₈	C₂×Dic₄₇	semidirect
351. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
353. C₄×Q₈	C₂×Dic₄₇	semidirect
484. Q₈	D₄×Dic₄₇	semidirect
485. D₄	#13093948	direct (N × H)
534. C₂²	C₂×#13093948	semidirect
550. C₄	C₂×#13093948	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
C₂²×#13093948	2
D₄×C₄⋊Dic₄₇	2
#20244312	2
#20244191	2
#20243812	2
#20243696	2
#20243393	2
#20243323	2
C₄×#13093948	2
C₂×D₄×Q₈×C₄₇	2
D₄×#103	47

Subgroups — D4×#13093948 #26231710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13093948 #26231710