Subgroups — C₂×#20243610 #26217121

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689172	C₂	1	2	yes	maximal, complemented
3	C₂×#15689090	C₂	1	1	yes	maximal, characteristic
4	#20243610	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688887	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic
7	#15689890	—	2	4	no	—
8	#15689890	—	2	2	no	—
9	#15689890	C₂²	1	4	yes	—
10	C₂×#13094031	—	2	4	no	—
11	C₂²×#10625329	—	2	2	no	—
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689172	—	2	4	no	—
16	#15689172	C₂²	1	8	yes	complemented
17	C₂×#13093960	—	2	4	no	—
18	#15689090	—	2	2	no	—
19	#15689090	C₂²	1	4	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
21	#15688887	C₂²	1	8	yes	complemented
22	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#413	C₄	1	4	yes	—
25	C₄₇×#413	C₂²	1	4	yes	—
26	C₂×#101×C₄₇	C₄	1	2	yes	—
27	C₂×#100×C₄₇	C₄	1	2	yes	—
28	#13094031	—	2	16	no	—
29	#13094031	—	2	16	no	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	2	8	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	8	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	1	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	D₄	1	4	yes	—
40	C₂×#10625329	D₄	1	4	yes	—
41	C₂×#10625329	C₂³	1	2	yes	—
42	C₂×#10625329	C₂³	1	4	yes	—
43	C₂²×C₄₇⋊C₈	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	—	2	1	no	—
47	C₂²×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	2	no	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	#13093960	—	2	16	no	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×#41×C₄₇	D₄	1	2	yes	—
59	C₂×#41×C₄₇	Q₈	1	2	yes	—
60	C₂×#41×C₄₇	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×D₄×C₄₇	Q₈	1	2	yes	—
64	C₂³×C₄×C₄₇	D₄	1	2	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
72	C₂²×C₈×C₄₇	—	2	2	no	—
73	#101×C₄₇	C₂×C₄	1	8	yes	—
74	#100×C₄₇	C₂×C₄	1	8	yes	—
75	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
76	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	—	2	4	no	—
84	#41×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
88	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₄₇	—	2	4	no	—
115	M₁₆×C₄₇	—	2	4	no	—
116	M₁₆×C₄₇	—	2	4	no	—
117	M₁₆×C₄₇	C₂²×C₄	1	8	yes	—
118	C₂×C₈×C₄₇	—	2	4	no	—
119	C₂×C₈×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	#10625329	—	2	16	no	—
122	#10625329	—	2	4	no	—
123	#10625329	—	2	4	no	—
124	#10625329	—	2	4	no	—
125	#10625329	—	2	4	no	—
126	#10625329	—	4	2	no	—
127	#10625329	C₂×D₄	1	8	yes	—
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	—	2	4	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	C₂×C₄₇⋊C₈	—	4	1	no	—
138	C₂×C₄₇⋊C₈	—	4	1	no	—
139	C₂×C₄₇⋊C₈	—	4	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
146	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
148	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₇	#120	1	2	yes	—
170	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#123	1	2	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
181	C₈×C₄₇	—	2	8	no	—
182	C₄₇⋊C₈	—	2	8	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	C₂×#1858	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	2	4	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	1	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	#385	1	1	yes	characteristic
196	C₂²×C₄₇	#385	1	2	yes	—
197	C₂²×C₄₇	#385	1	1	yes	characteristic
198	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
200	C₄×C₄₇	—	2	4	no	—
201	C₄×C₄₇	#385	1	1	yes	characteristic
202	C₄×C₄₇	#385	1	1	yes	characteristic
203	C₄×C₄₇	#385	1	2	yes	—
204	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
205	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
207	C₂×#568	—	47	1	no	—
208	C₂×#430	—	47	2	no	—
209	C₂×#413	D₄₇	1	1	yes	characteristic
210	C₂×#408	—	47	1	no	—
211	#1858	—	47	8	no	—
212	C₂×#341	—	47	2	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	—	4	4	no	—
218	C₂×C₄₇	#1858	1	2	yes	complemented
219	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
220	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
221	#568	—	47	4	no	—
222	#568	—	94	4	no	—
223	#568	—	94	2	no	—
224	C₂×#131	—	94	4	no	—
225	C₂²×M₁₆	—	47	2	no	—
226	C₂²×M₁₆	—	47	1	no	—
227	C₂²×M₁₆	—	94	2	no	—
228	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
229	C₂³×C₈	—	47	1	no	—
230	#430	—	47	8	no	—
231	#430	—	94	4	no	—
232	C₂×#108	—	94	4	no	—
233	#413	Dic₄₇	1	4	yes	—
234	#413	C₂×D₄₇	1	4	yes	—
235	C₂×#101	Dic₄₇	1	2	yes	—
236	C₂×#100	Dic₄₇	1	2	yes	—
237	#408	—	47	4	no	—
238	#408	—	94	2	no	—
239	C₂×C₂²⋊C₈	—	94	2	no	—
240	#341	—	47	8	no	—
241	C₄₇	C₂×#1858	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	2	2	no	—
243	C₂×#41	—	2	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	Dic₉₄	1	2	yes	—
247	C₂×#41	D₁₈₈	1	2	yes	—
248	C₂×#41	C₂×Dic₄₇	1	2	yes	—
249	C₂×#41	C₂²×D₄₇	1	2	yes	—
250	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
251	C₂²×D₄	Dic₉₄	1	2	yes	—
252	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
253	C₂³×C₄	D₁₈₈	1	2	yes	—
254	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
255	#131	—	94	16	no	—
256	#131	—	94	16	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	47	4	no	—
261	C₂×M₁₆	—	47	4	no	—
262	C₂×M₁₆	—	47	4	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	94	4	no	—
265	C₂×M₁₆	—	94	8	no	—
266	C₂×M₁₆	—	94	2	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	8	no	—
269	C₂×M₁₆	—	94	2	no	—
270	C₂×M₁₆	—	94	1	no	—
271	C₂×M₁₆	—	94	2	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
274	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
275	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	47	2	no	—
278	C₂²×C₈	—	94	4	no	—
279	C₂²×C₈	—	94	2	no	—
280	C₂²×C₈	—	94	1	no	—
281	C₂²×C₈	—	94	1	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	—	94	2	no	—
285	#108	—	94	16	no	—
286	#101	C₂×Dic₄₇	1	8	yes	—
287	#100	C₂×Dic₄₇	1	8	yes	—
288	C₂²⋊C₈	—	94	8	no	—
289	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
290	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
302	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
308	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
309	C₂×D₄	C₂×Dic₉₄	1	4	yes	—
310	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
316	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
317	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₄₇	1	2	yes	—
322	C₂²×C₄	D₄×D₄₇	1	2	yes	—
323	C₂²×C₄	#10625352	1	2	yes	—
324	C₂²×C₄	#10625352	1	2	yes	—
325	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	2	4	no	—
331	M₁₆	—	47	8	no	—
332	M₁₆	—	94	16	no	—
333	M₁₆	—	94	4	no	—
334	M₁₆	—	94	4	no	—
335	M₁₆	—	94	4	no	—
336	M₁₆	—	94	4	no	—
337	M₁₆	—	188	2	no	—
338	M₁₆	C₂²×Dic₄₇	1	8	yes	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	94	16	no	—
343	C₂×C₈	—	94	4	no	—
344	C₂×C₈	—	94	4	no	—
345	C₂×C₈	—	94	4	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	94	4	no	—
349	C₂×C₈	—	188	1	no	—
350	C₂×C₈	—	188	1	no	—
351	C₂×C₈	—	188	1	no	—
352	C₂×C₈	—	188	1	no	—
353	C₂×C₈	—	188	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
359	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
360	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
361	C₂³	#13094001	1	2	yes	—
362	C₂³	#13094001	1	2	yes	—
363	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
364	Q₈	—	2	4	no	—
365	Q₈	—	2	4	no	—
366	D₄	—	2	8	no	—
367	D₄	—	2	8	no	—
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
377	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
380	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
381	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
382	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
383	C₂×C₄	#13093994	1	2	yes	—
384	C₂×C₄	#13093994	1	1	yes	characteristic
385	C₂×C₄	#13093994	1	1	yes	characteristic
386	C₂×C₄	#13094001	1	2	yes	—
387	C₂×C₄	#13094001	1	2	yes	—
388	C₂×C₄	#13094008	1	1	yes	characteristic
389	C₂×C₄	#13094008	1	1	yes	characteristic
390	C₂×C₄	#13094008	1	2	yes	—
391	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
393	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625352	1	2	yes	—
395	C₈	—	2	8	no	—
396	C₈	—	94	8	no	—
397	C₈	—	188	2	no	—
398	C₈	—	188	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	2	no	—
408	C₂²	#15688998	1	1	yes	characteristic
409	C₂²	#15688998	1	2	yes	—
410	C₂²	#15688998	1	1	yes	characteristic
411	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
412	C₂²	C₂×#13094001	1	2	yes	—
413	C₄	—	2	4	no	—
414	C₄	#15688998	1	1	yes	characteristic
415	C₄	#15688998	1	1	yes	characteristic
416	C₄	#15688998	1	2	yes	—
417	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
418	C₄	C₂×#13093994	1	1	yes	characteristic
419	C₄	C₂×#13094008	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	—	4	4	no	—
425	C₂	#20243610	1	2	yes	direct product factor
426	C₂	C₂×#15688998	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#413	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#413	D₄₇
hypocenter	C₄₇	C₂×#1858
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
2. C₂×#15689172	C₂	semidirect
4. #20243610	C₂	direct (N × H)
5. C₂×#15688887	C₂	semidirect
16. #15689172	C₂²	semidirect
21. #15688887	C₂²	semidirect
218. C₂×C₄₇	#1858	semidirect
241. C₄₇	C₂×#1858	semidirect
425. C₂	#20243610	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×#15689890	2
C₂×#15689172	2
C₂×#15689090	2
#20243610	2
C₂×#15688887	2
C₂×C₄₇×#413	2
C₂×#1858	47

Subgroups — C2×#20243610 #26217121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243610 #26217121