Subgroups — C₂×#20244892 #26245327

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689022	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689019	C₂	1	1	yes	maximal, characteristic
5	#20244892	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688885	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×#13093955	—	2	4	no	—
16	C₂×#13093955	C₂²	1	4	yes	—
17	C₂×Dic₄₇⋊C₈	—	2	4	no	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
19	#15689022	—	2	2	no	—
20	#15689022	C₂²	1	4	yes	—
21	#15689019	—	2	2	no	—
22	#15689019	C₂²	1	4	yes	—
23	C₂×C₄₇⋊#95	—	2	1	no	—
24	C₂×C₄₇⋊#95	—	2	1	no	—
25	#15688886	C₂²	1	4	yes	—
26	#15688885	C₂²	1	4	yes	—
27	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#340	C₂²	1	4	yes	—
31	C₂³×Dic₄₇	—	2	1	no	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
34	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂×C₄⋊Dic₄₇	—	2	1	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	2	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	4	no	—
45	C₂×C₄⋊Dic₄₇	—	4	4	no	—
46	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	—	2	4	no	—
50	C₂×Dic₄₇⋊C₄	—	4	4	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	#13093955	—	2	8	no	—
56	Dic₄₇⋊C₈	—	2	8	no	—
57	C₄₇⋊#95	—	2	4	no	—
58	C₄₇⋊#95	—	2	4	no	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	—	2	1	no	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	2	2	no	—
65	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	—	4	2	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×C₄×C₄₇	#41	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	—	2	2	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂²×Dic₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
105	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
106	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	4	4	no	—
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	C₂×Q₈	1	4	yes	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	4	2	no	—
122	C₄⋊Dic₄₇	—	4	8	no	—
123	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
124	Dic₄₇⋊C₄	—	4	8	no	—
125	C₄×Dic₄₇	—	2	4	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	C₄×Dic₄₇	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	8	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
132	C₂³×C₄₇	#121	1	2	yes	—
133	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
134	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
135	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
136	C₂³×C₄₇	#135	1	2	yes	—
137	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
138	C₂³×C₄₇	#137	1	2	yes	—
139	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	8	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	8	4	no	—
148	C₂×C₄×C₄₇	#121	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	#123	1	4	yes	—
152	C₂×C₄×C₄₇	#125	1	4	yes	—
153	C₂×C₄×C₄₇	#125	1	4	yes	—
154	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	8	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	4	no	—
171	C₂×Dic₄₇	—	4	8	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	8	4	no	—
176	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
177	C₈×C₄₇	—	4	2	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	C₂×#2088	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	#398	1	4	yes	—
181	C₂²×C₄₇	#465	1	4	yes	—
182	C₂²×C₄₇	#468	1	4	yes	—
183	C₂²×C₄₇	#475	1	4	yes	—
184	C₂²×C₄₇	#476	1	4	yes	—
185	C₂²×C₄₇	#478	1	4	yes	—
186	C₂²×C₄₇	#479	1	4	yes	—
187	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	8	2	no	—
196	C₄×C₄₇	#398	1	4	yes	—
197	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
200	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	Dic₄₇	—	2	4	no	—
202	Dic₄₇	—	4	4	no	—
203	Dic₄₇	—	4	2	no	—
204	Dic₄₇	—	8	2	no	—
205	C₂²×#106	—	47	1	no	—
206	C₂²×C₄⋊C₈	—	47	1	no	—
207	C₂×#389	—	47	1	no	—
208	C₂×#389	—	47	1	no	—
209	#2088	—	47	8	no	—
210	C₂×#340	—	47	1	no	—
211	C₂×#340	—	47	1	no	—
212	C₂×#340	D₄₇	1	1	yes	characteristic
213	C₂×C₄₇	#2088	1	8	yes	complemented
214	C₂×C₄₇	C₂×#398	1	1	yes	characteristic
215	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#478	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#479	1	1	yes	characteristic
221	C₂³×C₈	—	47	1	no	—
222	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	—	47	1	no	—
224	C₂²×C₄⋊C₄	—	47	1	no	—
225	C₂²×C₄⋊C₄	—	94	1	no	—
226	C₂²×C₄⋊C₄	—	94	1	no	—
227	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
229	C₂²×C₄²	—	47	1	no	—
230	C₂×#106	—	47	4	no	—
231	C₂×#106	—	94	4	no	—
232	C₂×C₄⋊C₈	—	47	4	no	—
233	C₂×C₄⋊C₈	—	94	4	no	—
234	#389	—	47	4	no	—
235	#389	—	47	4	no	—
236	#389	—	94	2	no	—
237	#389	—	94	2	no	—
238	C₂×#95	—	94	1	no	—
239	C₂×#95	—	94	1	no	—
240	#340	—	47	4	no	—
241	#340	—	47	4	no	—
242	#340	C₂×D₄₇	1	4	yes	—
243	C₄₇	C₂×#2088	1	1	yes	characteristic, complemented, Sylow
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	47	1	no	—
247	C₂³×C₄	—	47	1	no	—
248	C₂³×C₄	—	94	1	no	—
249	C₂³×C₄	—	94	1	no	—
250	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	47	4	no	—
255	C₂²×C₈	—	47	2	no	—
256	C₂²×C₈	—	94	2	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	47	4	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	—	94	2	no	—
268	C₂×C₄⋊C₄	—	94	1	no	—
269	C₂×C₄⋊C₄	—	94	2	no	—
270	C₂×C₄⋊C₄	—	94	2	no	—
271	C₂×C₄⋊C₄	—	94	4	no	—
272	C₂×C₄⋊C₄	—	94	4	no	—
273	C₂×C₄⋊C₄	—	94	1	no	—
274	C₂×C₄⋊C₄	—	188	4	no	—
275	C₂×C₄⋊C₄	—	188	4	no	—
276	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
277	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
279	C₂×C₄²	—	47	2	no	—
280	C₂×C₄²	—	47	2	no	—
281	C₂×C₄²	—	94	2	no	—
282	C₂×C₄²	—	94	2	no	—
283	#106	—	94	8	no	—
284	C₄⋊C₈	—	94	8	no	—
285	#95	—	94	4	no	—
286	#95	—	94	4	no	—
287	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	47	4	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	—	94	2	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	94	4	no	—
303	C₂²×C₄	—	94	2	no	—
304	C₂²×C₄	—	94	2	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	2	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	—	188	2	no	—
310	C₂²×C₄	—	188	2	no	—
311	C₂²×C₄	—	188	2	no	—
312	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
313	C₂²×C₄	#10625350	1	2	yes	—
314	C₂²×C₄	#10625350	1	2	yes	—
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₄₇	1	2	yes	—
317	C₂²×C₄	#10625352	1	2	yes	—
318	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
319	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	—	47	4	no	—
325	C₂×C₈	—	94	8	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	47	4	no	—
334	C₄⋊C₄	—	94	4	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	94	2	no	—
337	C₄⋊C₄	—	94	2	no	—
338	C₄⋊C₄	—	188	8	no	—
339	C₄⋊C₄	—	188	8	no	—
340	C₄⋊C₄	—	188	2	no	—
341	C₄⋊C₄	C₂×Dic₉₄	1	4	yes	—
342	C₄²	—	94	4	no	—
343	C₄²	—	94	2	no	—
344	C₄²	—	94	2	no	—
345	C₂³	#13093997	1	2	yes	—
346	C₂³	#13094001	1	2	yes	—
347	C₂³	#13094002	1	2	yes	—
348	C₂³	SD₁₆×D₄₇	1	2	yes	—
349	C₂³	#13094047	1	2	yes	—
350	C₂³	#13094048	1	2	yes	—
351	C₂³	#13094053	1	2	yes	—
352	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	—	47	4	no	—
362	C₂×C₄	—	94	8	no	—
363	C₂×C₄	—	94	2	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	—	376	4	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	—	188	4	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	—	188	8	no	—
377	C₂×C₄	#13093997	1	2	yes	—
378	C₂×C₄	#13094001	1	2	yes	—
379	C₂×C₄	#13094002	1	2	yes	—
380	C₂×C₄	#13094006	1	4	yes	—
381	C₂×C₄	#13094014	1	4	yes	—
382	C₂×C₄	#13094016	1	4	yes	—
383	C₂×C₄	#13094023	1	4	yes	—
384	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	94	4	no	—
392	C₂²	#15689057	1	4	yes	—
393	C₂²	#15689355	1	4	yes	—
394	C₂²	#15689368	1	4	yes	—
395	C₂²	#15689407	1	4	yes	—
396	C₂²	#15689411	1	4	yes	—
397	C₂²	#15689426	1	4	yes	—
398	C₂²	#15689432	1	4	yes	—
399	C₂²	C₂×#13093997	1	1	yes	characteristic
400	C₂²	C₂×#13094001	1	1	yes	characteristic
401	C₂²	C₂×#13094002	1	1	yes	characteristic
402	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
403	C₂²	C₂×#13094047	1	1	yes	characteristic
404	C₂²	C₂×#13094048	1	1	yes	characteristic
405	C₂²	C₂×#13094053	1	1	yes	characteristic
406	C₄	—	4	4	no	—
407	C₄	—	8	2	no	—
408	C₄	—	94	4	no	—
409	C₄	—	376	2	no	—
410	C₄	—	188	2	no	—
411	C₄	—	188	4	no	—
412	C₄	#15689057	1	4	yes	—
413	C₄	C₂×#13094006	1	1	yes	characteristic
414	C₄	C₂×#13094014	1	1	yes	characteristic
415	C₄	C₂×#13094016	1	1	yes	characteristic
416	C₄	C₂×#13094023	1	1	yes	characteristic
417	C₂	#20244892	1	8	yes	direct product factor
418	C₂	C₂×#15689057	1	1	yes	characteristic
419	C₂	C₂×#15689355	1	1	yes	characteristic
420	C₂	C₂×#15689368	1	1	yes	characteristic
421	C₂	C₂×#15689411	1	1	yes	characteristic
422	C₂	C₂×#15689426	1	1	yes	characteristic
423	C₂	C₂×#15689407	1	1	yes	characteristic
424	C₂	C₂×#15689432	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×#2088
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. #20244892	C₂	direct (N × H)
213. C₂×C₄₇	#2088	semidirect
243. C₄₇	C₂×#2088	semidirect
417. C₂	#20244892	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×#13093955	2
C₂²×Dic₄₇⋊C₈	2
C₂×#15689022	2
C₂×#15689019	2
#20244892	2
C₂×#15688886	2
C₂×#15688885	2
C₂×C₄₇×#340	2
C₂×#2088	47

Subgroups — C2×#20244892 #26245327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244892 #26245327