Subgroups — C₂×#20242851 #26198769

Order 12032.

842 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×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689403	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242851	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625335	—	2	1	no	—
10	C₂²×#10625335	—	2	1	no	—
11	C₂²×#10625329	—	2	1	no	—
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	#15689495	—	2	2	no	—
14	#15689495	C₂²	1	4	yes	complemented
15	#15689403	—	2	2	no	—
16	#15689403	C₂²	1	4	yes	complemented
17	#15689201	—	2	2	no	—
18	#15689201	C₂²	1	4	yes	complemented
19	C₂×#13093957	—	2	1	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688875	C₂²	1	4	yes	complemented
26	#15688868	C₂²	1	4	yes	complemented
27	#15688867	C₂²	1	4	yes	complemented
28	C₂²×D₈×C₄₇	—	2	1	no	—
29	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#459	—	2	2	no	—
32	C₄₇×#459	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₇	—	2	1	no	—
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂×#10625335	—	2	4	no	—
37	C₂×#10625335	—	2	4	no	—
38	C₂×#10625335	—	4	4	no	—
39	C₂×#10625335	—	4	4	no	—
40	C₂×#10625329	—	2	4	no	—
41	C₂×#10625329	—	4	4	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	—	2	1	no	—
49	#13094024	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	—	2	1	no	—
52	#13093957	—	2	4	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093945	—	2	4	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
59	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	—	2	1	no	—
66	C₂×D₈×C₄₇	—	2	4	no	—
67	C₂×D₈×C₄₇	—	4	4	no	—
68	C₂²×C₈×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	—	2	1	no	—
71	#127×C₄₇	—	2	1	no	—
72	#127×C₄₇	C₂³	1	2	yes	—
73	C₄×D₄×C₄₇	—	2	1	no	—
74	C₄×D₄×C₄₇	—	2	1	no	—
75	C₄×D₄×C₄₇	D₄	1	2	yes	—
76	C₄×D₄×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	#102×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	2	1	no	—
84	C₂⁴×C₄₇	—	4	1	no	—
85	C₂×D₄×C₄₇	—	2	1	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	1	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	—	4	2	no	—
98	C₂×D₄×C₄₇	—	8	2	no	—
99	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	2	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	4	1	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	—	4	2	no	—
111	C₂×Dic₉₄	—	4	2	no	—
112	C₂×Dic₉₄	—	4	1	no	—
113	D₈×C₄₇	—	4	8	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	4	2	no	—
116	C₄⋊C₄×C₄₇	—	2	1	no	—
117	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	#41	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	#10625335	—	4	8	no	—
125	#10625335	—	4	8	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	4	1	no	—
129	C₄⋊Dic₄₇	—	4	1	no	—
130	#10625329	—	4	8	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂×C₄₇⋊C₈	—	4	2	no	—
136	C₂×C₄₇⋊C₈	D₈	1	4	yes	complemented
137	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
138	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	8	2	no	—
145	C₂³×C₄₇	—	8	2	no	—
146	C₂³×C₄₇	—	8	2	no	—
147	C₂³×C₄₇	#121	1	1	yes	characteristic
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	4	2	no	—
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	8	2	no	—
156	D₄×C₄₇	—	8	2	no	—
157	D₄×C₄₇	—	8	2	no	—
158	D₄×C₄₇	—	8	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
169	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₄₇	#137	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	8	2	no	—
177	Dic₉₄	—	4	2	no	—
178	Dic₉₄	—	4	2	no	—
179	Dic₉₄	—	8	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	C₂×D₈	1	4	yes	complemented
185	C₂×#1685	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	8	4	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	—	8	2	no	—
193	C₂²×C₄₇	—	16	4	no	—
194	C₂²×C₄₇	#459	1	2	yes	—
195	C₂²×C₄₇	#468	1	2	yes	—
196	C₂²×C₄₇	#471	1	2	yes	—
197	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	#459	1	2	yes	—
202	C₄×C₄₇	#468	1	2	yes	—
203	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
204	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
207	Dic₄₇	—	8	2	no	—
208	C₂×#492	—	47	1	no	—
209	C₂×#474	—	47	1	no	—
210	C₂×#459	D₄₇	1	1	yes	characteristic
211	C₂×#436	—	47	1	no	—
212	#1685	—	47	8	no	—
213	C₂×#335	—	47	1	no	—
214	C₂×#332	—	47	1	no	—
215	C₂×#331	—	47	1	no	—
216	C₂×C₄₇	—	8	2	no	—
217	C₂×C₄₇	—	16	2	no	—
218	C₂×C₄₇	#1685	1	4	yes	complemented
219	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
222	C₂²×SD₁₆	—	94	1	no	—
223	C₂²×SD₁₆	—	94	1	no	—
224	C₂²×D₈	—	2	1	no	—
225	C₂²×M₁₆	—	94	1	no	—
226	C₂×C₄⋊Q₈	—	47	1	no	—
227	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
229	#492	—	47	4	no	—
230	#492	—	94	2	no	—
231	#474	—	47	4	no	—
232	#474	—	94	2	no	—
233	#459	—	2	2	no	—
234	#459	C₂×D₄₇	1	4	yes	—
235	#436	—	47	4	no	—
236	#436	—	94	2	no	—
237	C₂×#107	—	94	1	no	—
238	C₂×C₄⋊C₈	—	47	1	no	—
239	C₂×C₄⋊C₈	—	47	1	no	—
240	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂×#102	—	2	1	no	—
242	C₂×#102	—	94	1	no	—
243	C₂×C₂²⋊C₈	—	94	1	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	#335	—	47	4	no	—
246	#332	—	47	4	no	—
247	#331	—	47	4	no	—
248	C₄₇	C₂×#1685	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	94	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
254	C₂³×C₄	—	2	1	no	—
255	C₂×SD₁₆	—	94	4	no	—
256	C₂×SD₁₆	—	94	4	no	—
257	C₂×SD₁₆	—	188	4	no	—
258	C₂×SD₁₆	—	188	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	—	4	4	no	—
261	C₂×M₁₆	—	94	4	no	—
262	C₂×M₁₆	—	188	4	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	94	1	no	—
267	C₂²×C₈	—	94	1	no	—
268	C₄⋊Q₈	—	47	2	no	—
269	C₄⋊Q₈	—	94	1	no	—
270	C₄⋊Q₈	—	94	1	no	—
271	C₄⋊Q₈	—	94	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	—	2	1	no	—
275	#127	C₂²×D₄₇	1	2	yes	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
279	C₄×D₄	C₂²×D₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	94	1	no	—
281	C₂×C₄⋊C₄	—	94	1	no	—
282	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	#107	—	94	4	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	47	2	no	—
288	C₄⋊C₈	—	47	2	no	—
289	C₄⋊C₈	—	94	1	no	—
290	C₄⋊C₈	—	94	1	no	—
291	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
292	#102	—	2	4	no	—
293	#102	—	94	4	no	—
294	C₂²⋊C₈	—	94	4	no	—
295	C₄×C₈	—	47	2	no	—
296	C₄×C₈	—	47	2	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂×Q₈	—	94	2	no	—
300	C₂×Q₈	—	188	2	no	—
301	C₂×Q₈	—	188	2	no	—
302	C₂×Q₈	—	188	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	8	2	no	—
317	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	188	1	no	—
324	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	#10625352	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	SD₁₆	—	188	8	no	—
328	SD₁₆	—	188	8	no	—
329	D₈	—	4	8	no	—
330	M₁₆	—	188	8	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	47	4	no	—
334	C₂×C₈	—	47	2	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	188	2	no	—
340	C₂×C₈	—	188	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	94	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	—	188	1	no	—
345	C₄⋊C₄	—	188	1	no	—
346	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₄²	D₄×D₄₇	1	1	yes	characteristic
350	C₄²	#10625352	1	1	yes	characteristic
351	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₄²	C₂³×D₄₇	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	#13093996	1	1	yes	characteristic
362	Q₈	—	376	2	no	—
363	Q₈	—	188	2	no	—
364	Q₈	—	188	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	376	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	#13093996	1	1	yes	characteristic
385	C₂×C₄	#13093996	1	1	yes	characteristic
386	C₂×C₄	#13093996	1	1	yes	characteristic
387	C₂×C₄	D₈×D₄₇	1	2	yes	—
388	C₂×C₄	#13094048	1	2	yes	—
389	C₂×C₄	#13094050	1	2	yes	—
390	C₂×C₄	#13094054	1	2	yes	—
391	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	47	4	no	—
396	C₈	—	94	2	no	—
397	C₈	—	188	2	no	—
398	C₈	—	188	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	4	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	16	4	no	—
407	C₂²	#15689316	1	2	yes	—
408	C₂²	#15689367	1	2	yes	—
409	C₂²	#15689384	1	2	yes	—
410	C₂²	C₂×#13093996	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	376	2	no	—
415	C₄	#15689316	1	2	yes	—
416	C₄	#15689367	1	2	yes	—
417	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
418	C₄	C₂×#13094048	1	1	yes	characteristic
419	C₄	C₂×#13094050	1	1	yes	characteristic
420	C₄	C₂×#13094054	1	1	yes	characteristic
421	C₂	—	8	2	no	—
422	C₂	—	16	2	no	—
423	C₂	#20242851	1	4	yes	direct product factor
424	C₂	C₂×#15689316	1	1	yes	characteristic
425	C₂	C₂×#15689367	1	1	yes	characteristic
426	C₂	C₂×#15689384	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#459	C₂
socle	C₂³×C₄₇	#121
hypercenter	C₂×#459	D₄₇
hypocenter	C₄₇	C₂×#1685
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#15689495	C₂	semidirect
2. C₂×#15689403	C₂	semidirect
3. C₂×#15689201	C₂	semidirect
4. #20242851	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
6. C₂×#15688868	C₂	semidirect
7. C₂×#15688867	C₂	semidirect
14. #15689495	C₂²	semidirect
16. #15689403	C₂²	semidirect
18. #15689201	C₂²	semidirect
25. #15688875	C₂²	semidirect
26. #15688868	C₂²	semidirect
27. #15688867	C₂²	semidirect
136. C₂×C₄₇⋊C₈	D₈	semidirect
184. C₄₇⋊C₈	C₂×D₈	semidirect
218. C₂×C₄₇	#1685	semidirect
248. C₄₇	C₂×#1685	semidirect
423. C₂	#20242851	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×#15689495	2
C₂×#15689403	2
C₂×#15689201	2
#20242851	2
C₂×#15688875	2
C₂×#15688868	2
C₂×#15688867	2
C₂×C₄₇×#459	2
C₂×#1685	47

Subgroups — C2×#20242851 #26198769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242851 #26198769