Subgroups — C₂×#20244720 #26244304

Order 12032.

1454 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094023	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689022	C₂	1	1	yes	maximal, characteristic
5	#20244720	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688885	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	—	2	1	no	—
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13094023	—	2	4	no	—
12	C₂×#13094023	—	2	2	no	—
13	C₂×#13094023	—	2	4	no	—
14	C₂×#13094023	C₂²	1	4	yes	—
15	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
16	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×#13093956	—	2	4	no	—
21	C₂×#13093956	C₂²	1	4	yes	—
22	C₂×#13093955	—	2	4	no	—
23	C₂×#13093955	C₂²	1	4	yes	—
24	#15689022	—	2	2	no	—
25	#15689022	C₂²	1	4	yes	—
26	C₂×C₄₇⋊#95	—	2	1	no	—
27	#15688885	C₂²	1	4	yes	—
28	#15688877	C₂²	1	4	yes	—
29	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#340	C₂²	1	4	yes	—
33	C₂²×Dic₉₄	—	2	8	no	—
34	C₂²×Dic₉₄	—	2	4	no	—
35	C₂²×Dic₉₄	—	4	4	no	—
36	C₂²×Dic₉₄	—	4	4	no	—
37	C₂³×Dic₄₇	—	2	1	no	—
38	C₂³×Dic₄₇	—	2	1	no	—
39	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
40	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	complemented
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	#13094023	—	2	16	no	—
46	#13094023	—	2	8	no	—
47	#13094023	—	2	8	no	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	—	4	4	no	—
55	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
58	C₂×Dic₄₇⋊C₄	—	2	8	no	—
59	C₂×Dic₄₇⋊C₄	—	2	4	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	#13093956	—	2	8	no	—
65	#13093955	—	2	8	no	—
66	C₄₇⋊#95	—	2	4	no	—
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂³×C₄×C₄₇	—	2	1	no	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	—	2	2	no	—
72	C₂²×C₈×C₄₇	Q₈	1	4	yes	complemented
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	complemented
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₄₇	#41	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	2	2	no	—
100	C₂²×Dic₄₇	—	2	2	no	—
101	C₂²×Dic₄₇	—	2	2	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	2	4	no	—
104	C₂²×Dic₄₇	—	2	2	no	—
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	4	2	no	—
107	C₂²×Dic₄₇	—	4	2	no	—
108	C₂²×Dic₄₇	—	4	2	no	—
109	C₂²×Dic₄₇	—	4	2	no	—
110	C₂²×Dic₄₇	—	4	2	no	—
111	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
112	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
113	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
114	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
115	C₂×Dic₉₄	—	2	16	no	—
116	C₂×Dic₉₄	—	4	8	no	—
117	C₂×Dic₉₄	—	4	32	no	—
118	C₂×Dic₉₄	—	4	8	no	—
119	C₂×C₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₄₇	C₂×Q₈	1	4	yes	complemented
129	C₄⋊Dic₄₇	—	2	4	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	4	2	no	—
134	C₄⋊Dic₄₇	—	4	8	no	—
135	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
136	Dic₄₇⋊C₄	—	2	16	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	8	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
144	C₂³×C₄₇	#120	1	2	yes	—
145	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
147	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
148	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
149	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
150	C₂³×C₄₇	#137	1	2	yes	—
151	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	8	no	—
160	C₂×C₄×C₄₇	#120	1	2	yes	—
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
164	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
165	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	2	8	no	—
178	C₂×Dic₄₇	—	2	8	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	8	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	2	no	—
186	C₂×Dic₄₇	—	8	4	no	—
187	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
188	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
189	Dic₉₄	—	4	32	no	—
190	C₈×C₄₇	—	2	4	no	—
191	C₄₇⋊C₈	—	2	4	no	—
192	C₂×#2058	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	#395	1	4	yes	—
194	C₂²×C₄₇	#448	1	4	yes	—
195	C₂²×C₄₇	#450	1	4	yes	—
196	C₂²×C₄₇	#475	1	4	yes	—
197	C₂²×C₄₇	#476	1	4	yes	—
198	C₂²×C₄₇	#498	1	4	yes	—
199	C₂²×C₄₇	#501	1	4	yes	—
200	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
203	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
204	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	4	no	—
209	C₄×C₄₇	#395	1	4	yes	—
210	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
213	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	Dic₄₇	—	2	4	no	—
215	Dic₄₇	—	2	4	no	—
216	Dic₄₇	—	4	4	no	—
217	Dic₄₇	—	8	2	no	—
218	C₂²×C₄⋊Q₈	—	47	1	no	—
219	C₂²×#106	—	47	1	no	—
220	C₂²×#106	—	47	1	no	—
221	C₂×#389	—	47	1	no	—
222	#2058	—	47	8	no	—
223	C₂×#340	—	47	1	no	—
224	C₂×#340	D₄₇	1	1	yes	characteristic
225	C₂×#336	—	47	1	no	—
226	C₂×C₄₇	#2058	1	8	yes	complemented
227	C₂×C₄₇	C₂×#395	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#498	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#501	1	1	yes	characteristic
234	C₂³×Q₈	—	94	1	no	—
235	C₂³×C₈	—	47	1	no	—
236	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	—	47	4	no	—
238	C₂×C₄⋊Q₈	—	94	2	no	—
239	C₂×C₄⋊Q₈	—	94	4	no	—
240	C₂×C₄⋊Q₈	—	94	4	no	—
241	C₂²×C₄⋊C₄	—	47	1	no	—
242	C₂²×C₄⋊C₄	—	47	1	no	—
243	C₂²×C₄⋊C₄	—	94	1	no	—
244	C₂²×C₄⋊C₄	—	94	1	no	—
245	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
247	C₂²×C₄²	—	47	1	no	—
248	C₂×#106	—	47	4	no	—
249	C₂×#106	—	47	4	no	—
250	C₂×#106	—	94	4	no	—
251	C₂×#106	—	94	4	no	—
252	#389	—	47	4	no	—
253	#389	—	94	2	no	—
254	C₂×#95	—	94	1	no	—
255	#340	—	47	4	no	—
256	#340	C₂×D₄₇	1	4	yes	—
257	#336	—	47	4	no	—
258	C₄₇	C₂×#2058	1	1	yes	characteristic, complemented, Sylow
259	C₂²×Q₈	—	94	4	no	—
260	C₂²×Q₈	—	94	8	no	—
261	C₂²×Q₈	—	188	4	no	—
262	C₂²×Q₈	—	188	4	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	47	1	no	—
266	C₂³×C₄	—	47	1	no	—
267	C₂³×C₄	—	94	1	no	—
268	C₂³×C₄	—	94	1	no	—
269	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	—	47	4	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	94	2	no	—
275	C₂²×C₈	—	94	2	no	—
276	C₂²×C₈	Dic₉₄	1	4	yes	complemented
277	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
278	C₄⋊Q₈	—	94	8	no	—
279	C₄⋊Q₈	—	94	16	no	—
280	C₄⋊Q₈	—	94	8	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	47	4	no	—
286	C₂×C₄⋊C₄	—	47	2	no	—
287	C₂×C₄⋊C₄	—	47	2	no	—
288	C₂×C₄⋊C₄	—	94	4	no	—
289	C₂×C₄⋊C₄	—	94	8	no	—
290	C₂×C₄⋊C₄	—	94	2	no	—
291	C₂×C₄⋊C₄	—	94	1	no	—
292	C₂×C₄⋊C₄	—	94	2	no	—
293	C₂×C₄⋊C₄	—	94	2	no	—
294	C₂×C₄⋊C₄	—	94	4	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	188	4	no	—
297	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	complemented
298	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
299	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
301	C₂×C₄²	—	47	2	no	—
302	C₂×C₄²	—	47	2	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	—	94	2	no	—
305	#106	—	94	8	no	—
306	#106	—	94	8	no	—
307	#95	—	94	4	no	—
308	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
309	C₂×Q₈	—	94	16	no	—
310	C₂×Q₈	—	188	8	no	—
311	C₂×Q₈	—	188	32	no	—
312	C₂×Q₈	—	188	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	47	4	no	—
322	C₂²×C₄	—	47	4	no	—
323	C₂²×C₄	—	47	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	—	94	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	94	4	no	—
330	C₂²×C₄	—	94	2	no	—
331	C₂²×C₄	—	94	2	no	—
332	C₂²×C₄	—	188	2	no	—
333	C₂²×C₄	—	188	2	no	—
334	C₂²×C₄	—	188	2	no	—
335	C₂²×C₄	—	188	2	no	—
336	C₂²×C₄	—	188	2	no	—
337	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
338	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
339	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
340	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₄₇	1	2	yes	—
342	C₂²×C₄	#10625352	1	2	yes	—
343	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	C₂×C₈	—	2	8	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	47	4	no	—
349	C₂×C₈	—	94	8	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	C₂×Dic₉₄	1	4	yes	complemented
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	47	4	no	—
358	C₄⋊C₄	—	94	16	no	—
359	C₄⋊C₄	—	94	4	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	—	94	2	no	—
362	C₄⋊C₄	—	94	2	no	—
363	C₄⋊C₄	—	188	8	no	—
364	C₄⋊C₄	—	188	2	no	—
365	C₄⋊C₄	C₂×Dic₉₄	1	4	yes	complemented
366	C₄⋊C₄	C₂×D₁₈₈	1	4	yes	—
367	C₄²	—	94	4	no	—
368	C₄²	—	94	2	no	—
369	C₄²	—	94	2	no	—
370	C₂³	#13093994	1	2	yes	—
371	C₂³	#13094001	1	2	yes	—
372	C₂³	#13094023	1	2	yes	—
373	C₂³	SD₁₆×D₄₇	1	2	yes	—
374	C₂³	SD₁₆×D₄₇	1	2	yes	—
375	C₂³	#13094048	1	2	yes	—
376	C₂³	#13094056	1	2	yes	—
377	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
378	Q₈	—	188	32	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	47	4	no	—
388	C₂×C₄	—	47	4	no	—
389	C₂×C₄	—	94	8	no	—
390	C₂×C₄	—	94	8	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	4	no	—
396	C₂×C₄	—	376	4	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	—	188	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	8	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	#13093994	1	2	yes	—
404	C₂×C₄	#13094001	1	2	yes	—
405	C₂×C₄	#13094001	1	4	yes	—
406	C₂×C₄	#13094004	1	4	yes	—
407	C₂×C₄	#13094023	1	2	yes	—
408	C₂×C₄	#13094023	1	4	yes	—
409	C₂×C₄	#13094024	1	4	yes	—
410	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
412	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
414	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	94	4	no	—
418	C₂²	#15689044	1	4	yes	—
419	C₂²	#15689263	1	4	yes	—
420	C₂²	#15689275	1	4	yes	—
421	C₂²	#15689406	1	4	yes	—
422	C₂²	#15689411	1	4	yes	—
423	C₂²	#15689520	1	4	yes	—
424	C₂²	#15689531	1	4	yes	—
425	C₂²	C₂×#13093994	1	1	yes	characteristic
426	C₂²	C₂×#13094001	1	1	yes	characteristic
427	C₂²	C₂×#13094023	1	1	yes	characteristic
428	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
429	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
430	C₂²	C₂×#13094048	1	1	yes	characteristic
431	C₂²	C₂×#13094056	1	1	yes	characteristic
432	C₄	—	4	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	94	4	no	—
435	C₄	—	94	4	no	—
436	C₄	—	376	2	no	—
437	C₄	—	188	4	no	—
438	C₄	#15689044	1	4	yes	—
439	C₄	C₂×#13094001	1	1	yes	characteristic
440	C₄	C₂×#13094004	1	1	yes	characteristic
441	C₄	C₂×#13094023	1	1	yes	characteristic
442	C₄	C₂×#13094024	1	1	yes	characteristic
443	C₂	#20244720	1	8	yes	direct product factor
444	C₂	C₂×#15689044	1	1	yes	characteristic
445	C₂	C₂×#15689275	1	1	yes	characteristic
446	C₂	C₂×#15689263	1	1	yes	characteristic
447	C₂	C₂×#15689411	1	1	yes	characteristic
448	C₂	C₂×#15689406	1	1	yes	characteristic
449	C₂	C₂×#15689520	1	1	yes	characteristic
450	C₂	C₂×#15689531	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	C₂×#2058
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
5. #20244720	C₂	direct (N × H)
43. C₂²×C₄₇⋊C₈	Q₈	semidirect
72. C₂²×C₈×C₄₇	Q₈	semidirect
79. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
122. C₂×C₈×C₄₇	C₂×Q₈	semidirect
128. C₄⋊C₄×C₄₇	C₂×Q₈	semidirect
143. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
226. C₂×C₄₇	#2058	semidirect
258. C₄₇	C₂×#2058	semidirect
276. C₂²×C₈	Dic₉₄	semidirect
297. C₂×C₄⋊C₄	Dic₉₄	semidirect
352. C₂×C₈	C₂×Dic₉₄	semidirect
365. C₄⋊C₄	C₂×Dic₉₄	semidirect
443. C₂	#20244720	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094023	2
C₂²×#13093956	2
C₂²×#13093955	2
C₂×#15689022	2
#20244720	2
C₂×#15688885	2
C₂×#15688877	2
C₂×C₄₇×#340	2
C₂×#2058	47

Subgroups — C2×#20244720 #26244304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244720 #26244304