Subgroups — D₄×#13093934 #26214737

Order 12032.

1274 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#13093934	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243167	C₂	1	2	yes	maximal, complemented
8	#20243164	C₂	1	2	yes	maximal, complemented
9	#20243152	C₂	1	2	yes	maximal, complemented
10	C₄×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₄	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
15	D₄×C₄₇⋊C₈	C₄	1	8	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×#13093934	—	2	8	no	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×#13093934	C₂²	1	2	yes	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×#13093934	C₂²	1	1	yes	characteristic
24	C₂×#13093934	C₂²	1	1	yes	characteristic
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₂²⋊C₄×Dic₄₇	C₄	1	4	yes	—
30	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₈×D₄×C₄₇	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
42	C₂²×C₄₇⋊C₈	—	2	4	no	—
43	C₂²×C₄₇⋊C₈	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	D₄×Dic₄₇	—	2	8	no	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₄×Dic₄₇	—	2	4	no	—
52	C₂×C₄×Dic₄₇	—	2	4	no	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
60	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
61	#13093934	—	2	4	no	—
62	#13093934	—	2	2	no	—
63	#13093934	—	2	4	no	—
64	#13093934	—	2	2	no	—
65	#13093934	—	2	4	no	—
66	#13093934	—	2	2	no	—
67	#13093934	D₄	1	4	yes	direct product factor
68	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
69	C₄₇⋊#95	C₂×C₄	1	4	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	—	2	4	no	—
74	C₂²×C₈×C₄₇	—	2	4	no	—
75	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
85	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
87	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₄₇	C₄²	1	4	yes	—
89	C₂×D₄×C₄₇	M₁₆	1	8	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	8	no	—
101	C₂²×Dic₄₇	—	2	8	no	—
102	C₂²×Dic₄₇	—	4	4	no	—
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	16	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₇	#41	1	2	yes	—
116	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
117	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂²⋊Dic₄₇	—	2	8	no	—
121	C₄⋊Dic₄₇	—	2	4	no	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	1	no	—
125	C₄×Dic₄₇	—	2	1	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	C₄×Dic₄₇	—	2	8	no	—
128	C₄×Dic₄₇	—	4	2	no	—
129	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
130	C₄×Dic₄₇	#41	1	2	yes	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	16	no	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	#41	1	2	yes	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
145	C₂³×C₄₇	C₂×M₁₆	1	8	yes	—
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	D₄×C₄₇	#97	1	16	yes	complemented
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	4	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	4	no	—
173	C₂×Dic₄₇	—	4	16	no	—
174	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
175	C₈×C₄₇	—	2	4	no	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
178	C₄₇⋊C₈	—	2	4	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	C₄×D₄	1	4	yes	complemented
181	D₄×#97	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	2	8	no	—
184	C₂²×C₄₇	—	2	8	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	C₂×#97	1	8	yes	complemented
187	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
190	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
191	C₂²×C₄₇	#568	1	2	yes	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	2	4	no	—
194	C₄×C₄₇	C₂×#97	1	4	yes	complemented
195	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
198	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
199	Dic₄₇	—	2	4	no	—
200	Dic₄₇	—	4	4	no	—
201	Dic₄₇	—	4	2	no	—
202	C₂×C₈×D₄	—	47	1	no	—
203	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic
204	C₂²×#97	—	47	2	no	—
205	C₄²×D₄	—	47	1	no	—
206	#1770	—	47	1	no	—
207	#1770	—	47	1	no	—
208	#1767	—	47	1	no	—
209	#1752	—	47	2	no	—
210	#1752	—	47	2	no	—
211	#1749	—	47	2	no	—
212	C₄×#97	—	47	1	no	—
213	C₂×C₄₇	—	2	8	no	—
214	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
215	C₂×C₄₇	C₂²×#97	1	1	yes	characteristic
216	C₂×C₄₇	#2875	1	1	yes	characteristic
217	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
218	C₂×C₄₇	#2970	1	2	yes	—
219	C₂³×C₈	—	47	2	no	—
220	C₂³×C₈	C₂×D₄₇	1	2	yes	—
221	C₂×C₄×D₄	—	47	2	no	—
222	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
223	C₂²×C₄²	—	47	2	no	—
224	C₈×D₄	—	47	8	no	—
225	C₈×D₄	Dic₄₇	1	8	yes	complemented
226	C₂×C₄⋊C₈	—	47	1	no	—
227	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
228	C₂×C₂²⋊C₈	—	47	2	no	—
229	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
230	C₂×#97	—	47	1	no	—
231	C₂×#97	—	47	2	no	—
232	C₂×#97	—	47	2	no	—
233	C₂×#97	—	47	2	no	—
234	C₂×#97	—	47	1	no	—
235	C₂×#97	—	47	1	no	—
236	C₂×#97	—	47	1	no	—
237	C₂×#97	—	94	8	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
240	C₄×C₄⋊C₄	—	47	2	no	—
241	C₄×C₄⋊C₄	—	47	1	no	—
242	C₄×C₂²⋊C₄	—	47	2	no	—
243	C₄×C₂²⋊C₄	—	47	4	no	—
244	C₄³	—	47	1	no	—
245	#336	—	47	2	no	—
246	#336	—	47	2	no	—
247	#336	—	47	2	no	—
248	C₄₇	D₄×#97	1	1	yes	characteristic, complemented, Sylow
249	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
250	C₂³×C₄	—	47	4	no	—
251	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	—	47	8	no	—
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	94	4	no	—
259	C₂²×C₈	—	94	4	no	—
260	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
261	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
262	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	C₄×D₄	—	94	8	no	—
265	C₄×D₄	C₄×D₄₇	1	4	yes	—
266	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
267	C₂×C₄⋊C₄	—	47	2	no	—
268	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	47	4	no	—
270	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	2	no	—
273	C₂×C₄²	—	47	4	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	47	2	no	—
276	C₂×C₄²	—	47	2	no	—
277	C₂×C₄²	—	94	4	no	—
278	C₂×C₄²	—	94	4	no	—
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
280	C₄⋊C₈	—	47	4	no	—
281	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
282	C₂²⋊C₈	—	47	8	no	—
283	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
284	#97	—	47	4	no	—
285	#97	—	94	2	no	—
286	#97	—	94	4	no	—
287	#97	—	94	2	no	—
288	#97	—	94	4	no	—
289	#97	—	94	4	no	—
290	#97	—	94	2	no	—
291	C₄×C₈	—	47	4	no	—
292	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
293	#95	—	47	4	no	—
294	#95	—	47	2	no	—
295	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
296	C₂×D₄	#10625324	1	8	yes	—
297	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	—	47	4	no	—
305	C₂²×C₄	—	94	8	no	—
306	C₂²×C₄	—	94	8	no	—
307	C₂²×C₄	—	188	4	no	—
308	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
311	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
313	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	16	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	47	2	no	—
321	C₂×C₈	—	47	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	4	no	—
324	C₂×C₈	—	94	16	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	D₄×D₄₇	1	2	yes	—
330	C₂×C₈	#10625352	1	2	yes	—
331	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
332	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
333	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
336	C₂²⋊C₄	—	94	8	no	—
337	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
338	C₄²	—	47	2	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	94	8	no	—
341	C₄²	—	94	4	no	—
342	C₄²	—	94	2	no	—
343	C₄²	—	94	1	no	—
344	C₄²	—	94	2	no	—
345	C₄²	—	94	1	no	—
346	C₄²	—	188	2	no	—
347	C₄²	C₂×C₄×D₄₇	1	2	yes	—
348	C₄²	C₂²×Dic₄₇	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
353	C₂³	C₂×#10625324	1	8	yes	—
354	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
355	D₄	#13093934	1	16	yes	direct product factor
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	47	4	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	4	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	4	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	4	no	—
372	C₂×C₄	—	188	16	no	—
373	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
374	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
375	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
376	C₂×C₄	C₂×#10625324	1	4	yes	—
377	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	2	no	—
385	C₈	—	47	4	no	—
386	C₈	—	94	4	no	—
387	C₈	—	94	2	no	—
388	C₈	D₄×Dic₄₇	1	4	yes	complemented
389	C₂²	—	2	4	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	8	no	—
393	C₂²	C₂×#13093934	1	8	yes	complemented
394	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
396	C₂²	C₄×#10625352	1	1	yes	characteristic
397	C₂²	C₂²×#10625324	1	2	yes	—
398	C₂²	#15689888	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	94	4	no	—
402	C₄	—	188	4	no	—
403	C₄	—	188	2	no	—
404	C₄	C₂×#13093934	1	4	yes	complemented
405	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
406	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
407	C₄	C₄×#10625352	1	1	yes	characteristic
408	C₄	#41×Dic₄₇	1	1	yes	characteristic
409	C₂	—	2	8	no	—
410	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
411	C₂	C₂²×#13093934	1	1	yes	characteristic
412	C₂	#20251814	1	1	yes	characteristic
413	C₂	D₄×#10625324	1	2	yes	—
414	C₂	#20252396	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	D₄×#97
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093934	C₂	semidirect
4. #20243258	C₂	semidirect
5. #20243255	C₂	semidirect
6. #20243243	C₂	semidirect
7. #20243167	C₂	semidirect
8. #20243164	C₂	semidirect
9. #20243152	C₂	semidirect
10. C₄×#13093934	C₂	semidirect
15. D₄×C₄₇⋊C₈	C₄	semidirect
37. C₈×D₄×C₄₇	C₄	semidirect
44. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
59. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
60. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
67. #13093934	D₄	direct (N × H)
68. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
75. C₂²×C₈×C₄₇	C₂×C₄	semidirect
84. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
85. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
86. C₄×C₈×C₄₇	C₂×C₄	semidirect
147. D₄×C₄₇	#97	semidirect
177. C₈×C₄₇	C₄×D₄	semidirect
180. C₄₇⋊C₈	C₄×D₄	semidirect
186. C₂²×C₄₇	C₂×#97	semidirect
194. C₄×C₄₇	C₂×#97	semidirect
225. C₈×D₄	Dic₄₇	semidirect
248. C₄₇	D₄×#97	semidirect
260. C₂²×C₈	C₂×Dic₄₇	semidirect
281. C₄⋊C₈	C₂×Dic₄₇	semidirect
283. C₂²⋊C₈	C₂×Dic₄₇	semidirect
292. C₄×C₈	C₂×Dic₄₇	semidirect
355. D₄	#13093934	direct (N × H)
388. C₈	D₄×Dic₄₇	semidirect
393. C₂²	C₂×#13093934	semidirect
404. C₄	C₂×#13093934	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×#13093934	2
C₄×D₄×Dic₄₇	2
#20243258	2
#20243255	2
#20243243	2
#20243167	2
#20243164	2
#20243152	2
C₄×#13093934	2
C₂×C₈×D₄×C₄₇	2
D₄×#97	47

Subgroups — D4×#13093934 #26214737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#13093934 #26214737