Subgroups — C₂×#20241843 #26182879

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20241843	C₂	1	8	yes	maximal, direct product factor
4	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	1	no	—
7	C₂³×C₄₇⋊C₈	—	2	1	no	—
8	#15689147	—	2	2	no	—
9	#15689147	C₂²	1	4	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
13	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
16	Q₈⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
17	C₄₇×#533	—	2	2	no	—
18	C₄₇×#533	—	2	2	no	—
19	C₄₇×#533	C₄	1	4	yes	—
20	C₄₇×#533	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
23	C₂×#125×C₄₇	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
26	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
27	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
28	C₂×#117×C₄₇	—	2	1	no	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	4	4	no	—
32	C₂²×C₄₇⋊C₈	—	2	8	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
38	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
39	C₄×C₄₇⋊C₈	—	2	2	no	—
40	C₄×C₄₇⋊C₈	—	2	4	no	—
41	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
42	C₂²×Q₈×C₄₇	—	2	1	no	—
43	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₄⋊Q₈×C₄₇	—	2	2	no	—
49	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
50	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
51	#125×C₄₇	—	2	4	no	—
52	#125×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	4	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
57	C₄×Q₈×C₄₇	—	2	4	no	—
58	C₄×Q₈×C₄₇	—	2	4	no	—
59	C₄×Q₈×C₄₇	—	2	2	no	—
60	C₄×Q₈×C₄₇	—	2	2	no	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
63	#117×C₄₇	—	2	4	no	—
64	#117×C₄₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
81	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	4	no	—
84	C₂×Q₈×C₄₇	—	2	8	no	—
85	C₂×Q₈×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
97	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
98	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	8	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₂²⋊C₄×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	4	no	—
116	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
118	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂×D₄	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
126	#10625329	—	4	8	no	—
127	C₂×C₄₇⋊C₈	—	2	8	no	—
128	C₂×C₄₇⋊C₈	—	2	16	no	—
129	C₂×C₄₇⋊C₈	—	2	4	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	#103	1	4	yes	—
135	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	Q₈×C₄₇	—	2	8	no	—
138	Q₈×C₄₇	—	4	4	no	—
139	Q₈×C₄₇	—	4	8	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	#103	1	8	yes	—
151	C₂×C₄×C₄₇	#103	1	4	yes	—
152	C₂×C₄×C₄₇	#104	1	4	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	#131	1	4	yes	—
160	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₄₇⋊C₈	—	2	8	no	—
168	C₄₇⋊C₈	—	4	4	no	—
169	C₂×#1493	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	8	no	—
173	C₂²×C₄₇	#408	1	2	yes	—
174	C₂²×C₄₇	C₂×#103	1	4	yes	—
175	C₂²×C₄₇	C₂×#103	1	2	yes	—
176	C₂²×C₄₇	C₂×#104	1	2	yes	—
177	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	—	4	4	no	—
183	C₄×C₄₇	#408	1	2	yes	—
184	C₄×C₄₇	C₂×#103	1	2	yes	—
185	C₄×C₄₇	C₂×#103	1	4	yes	—
186	C₄×C₄₇	C₂×#104	1	4	yes	—
187	C₄×C₄₇	C₂×#131	1	2	yes	—
188	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
189	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
190	C₂×#533	D₄₇	1	1	yes	characteristic
191	C₂×#423	—	47	1	no	—
192	C₂²×C₄×C₈	—	47	1	no	—
193	#1493	—	47	8	no	—
194	C₂×Q₈⋊C₈	—	47	4	no	—
195	C₂×C₄₇	—	2	4	no	—
196	C₂×C₄₇	#1493	1	4	yes	complemented
197	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
198	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
199	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
200	C₂²×M₁₆	—	94	1	no	—
201	C₂³×C₈	—	94	1	no	—
202	#533	—	2	2	no	—
203	#533	—	2	2	no	—
204	#533	Dic₄₇	1	4	yes	—
205	#533	C₂×D₄₇	1	4	yes	—
206	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
208	C₂×#125	—	2	1	no	—
209	C₂×C₂²⋊Q₈	—	2	1	no	—
210	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
213	C₂×#117	—	2	1	no	—
214	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
215	#423	—	47	4	no	—
216	#423	—	94	2	no	—
217	C₂×C₄⋊C₈	—	47	2	no	—
218	C₂×C₄⋊C₈	—	94	1	no	—
219	C₂×C₄×C₈	—	47	2	no	—
220	C₂×C₄×C₈	—	47	4	no	—
221	C₂×C₄×C₈	—	94	1	no	—
222	C₂×C₄×C₈	—	94	2	no	—
223	Q₈⋊C₈	—	47	16	no	—
224	C₄₇	C₂×#1493	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₈	—	2	1	no	—
226	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
227	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
230	C₂×M₁₆	—	94	4	no	—
231	C₂×M₁₆	—	188	4	no	—
232	C₂²×C₈	—	94	8	no	—
233	C₂²×C₈	—	94	2	no	—
234	C₂²×C₈	—	94	4	no	—
235	C₂²×C₈	—	94	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
239	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
240	#125	—	2	4	no	—
241	#125	—	2	4	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	C₂×Dic₄₇	1	4	yes	—
251	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
252	#117	—	2	4	no	—
253	#117	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
266	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
267	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₄⋊C₈	—	47	4	no	—
271	C₄⋊C₈	—	94	2	no	—
272	C₄⋊C₈	—	94	4	no	—
273	C₄×C₈	—	47	4	no	—
274	C₄×C₈	—	94	2	no	—
275	C₄×C₈	—	94	4	no	—
276	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	#10625336	1	4	yes	—
287	C₂²×C₄	#10625337	1	4	yes	—
288	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
289	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
293	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	M₁₆	—	188	8	no	—
301	C₂×C₈	—	94	8	no	—
302	C₂×C₈	—	94	16	no	—
303	C₂×C₈	—	94	4	no	—
304	C₂×C₈	—	94	4	no	—
305	C₂×C₈	—	188	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
314	C₂²⋊C₄	—	2	8	no	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
318	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
319	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
320	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
321	C₄²	C₂²×Dic₄₇	1	2	yes	—
322	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
324	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
326	C₄²	C₂³×D₄₇	1	1	yes	characteristic
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	#13093948	1	4	yes	—
330	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
331	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	Q₈	—	2	8	no	—
333	Q₈	—	4	4	no	—
334	Q₈	—	4	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	#13093948	1	8	yes	—
346	C₂×C₄	#13093948	1	4	yes	—
347	C₂×C₄	#13093951	1	4	yes	—
348	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
350	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
354	C₂×C₄	#13094031	1	4	yes	—
355	C₂×C₄	C₂×#10625336	1	2	yes	—
356	C₂×C₄	C₂×#10625336	1	4	yes	—
357	C₂×C₄	C₂×#10625337	1	4	yes	—
358	C₂×C₄	C₂×#10625337	1	2	yes	—
359	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
362	C₈	—	94	8	no	—
363	C₈	—	188	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	2	no	—
367	C₂²	#15689090	1	2	yes	—
368	C₂²	C₂×#13093948	1	4	yes	—
369	C₂²	C₂×#13093948	1	2	yes	—
370	C₂²	C₂×#13093951	1	2	yes	—
371	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	2	no	—
375	C₄	—	4	4	no	—
376	C₄	—	4	4	no	—
377	C₄	#15689090	1	2	yes	—
378	C₄	C₂×#13093948	1	2	yes	—
379	C₄	C₂×#13093948	1	4	yes	—
380	C₄	C₂×#13093951	1	4	yes	—
381	C₄	C₂×#13094031	1	2	yes	—
382	C₄	C₂²×#10625336	1	1	yes	characteristic
383	C₄	C₂²×#10625337	1	1	yes	characteristic
384	C₂	—	2	4	no	—
385	C₂	#20241843	1	4	yes	direct product factor
386	C₂	C₂×#15689090	1	1	yes	characteristic
387	C₂	C₂²×#13093948	1	1	yes	characteristic
388	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	C₂×#1493
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20241843	C₂	direct (N × H)
4. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
16. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
196. C₂×C₄₇	#1493	semidirect
224. C₄₇	C₂×#1493	semidirect
385. C₂	#20241843	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×#15689147	2
C₂²×C₄×C₄₇⋊C₈	2
#20241843	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#533	2
C₂×#1493	47

Subgroups — C2×#20241843 #26182879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241843 #26182879