Subgroups — C₂×#20242951 #26198845

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689318	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242951	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688866	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625334	—	2	1	no	—
10	C₂²×#10625329	—	2	1	no	—
11	C₂×#13094021	C₂²	1	1	yes	characteristic
12	#15689471	—	2	2	no	—
13	#15689471	C₂²	1	4	yes	complemented
14	#15689318	—	2	2	no	—
15	#15689318	C₂²	1	4	yes	—
16	#15689201	—	2	2	no	—
17	#15689201	C₂²	1	4	yes	complemented
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093944	—	2	1	no	—
21	C₂×#13093944	—	2	1	no	—
22	C₂×#13093944	—	2	1	no	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688873	C₂²	1	4	yes	complemented
26	#15688869	C₂²	1	4	yes	complemented
27	#15688866	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#461	—	2	2	no	—
32	C₄₇×#461	C₂²	1	4	yes	complemented
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₇	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂×#10625334	—	2	4	no	—
39	C₂×#10625334	—	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	#13094021	—	2	1	no	—
47	#13094021	—	2	1	no	—
48	#13094021	—	2	1	no	—
49	#13094021	C₂³	1	2	yes	—
50	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
54	#13093944	—	2	4	no	—
55	#13093944	—	2	4	no	—
56	#13093944	—	2	4	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
58	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂²×Q₈×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	1	no	—
63	C₂×SD₁₆×C₄₇	—	2	4	no	—
64	C₂×SD₁₆×C₄₇	—	4	4	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	—	2	1	no	—
69	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
70	C₄×D₄×C₄₇	—	2	1	no	—
71	C₄×D₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	D₄	1	2	yes	—
73	C₄×D₄×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	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
81	#103×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	1	no	—
83	C₂³×D₄₇	—	4	1	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	4	1	no	—
86	C₂×Q₈×C₄₇	—	4	2	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×D₄×C₄₇	—	2	1	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	4	2	no	—
96	C₂²×C₄×C₄₇	—	4	2	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂×D₁₈₈	—	2	2	no	—
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×D₁₈₈	—	2	2	no	—
104	C₂×D₁₈₈	—	4	2	no	—
105	C₂×D₁₈₈	—	4	2	no	—
106	C₂×D₁₈₈	—	4	2	no	—
107	C₂×D₁₈₈	—	4	2	no	—
108	C₂×D₁₈₈	—	4	1	no	—
109	C₂×D₁₈₈	—	4	1	no	—
110	C₂×D₁₈₈	—	4	1	no	—
111	C₂×D₁₈₈	—	8	2	no	—
112	SD₁₆×C₄₇	—	4	8	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	2	1	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	4	1	no	—
119	C₄⋊C₄×C₄₇	—	4	1	no	—
120	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₇	#41	1	1	yes	characteristic
126	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
127	#10625334	—	4	8	no	—
128	#10625329	—	4	8	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	4	2	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
136	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	#121	1	1	yes	characteristic
142	C₂²×D₄₇	—	4	2	no	—
143	C₂²×D₄₇	—	8	2	no	—
144	C₂²×D₄₇	—	8	2	no	—
145	C₂²×D₄₇	—	8	2	no	—
146	Q₈×C₄₇	—	4	2	no	—
147	Q₈×C₄₇	—	4	2	no	—
148	Q₈×C₄₇	—	8	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	2	2	no	—
151	D₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	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	4	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	8	2	no	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#135	1	2	yes	—
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	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	C₂×#41	1	1	yes	characteristic
170	D₁₈₈	—	4	2	no	—
171	D₁₈₈	—	4	2	no	—
172	D₁₈₈	—	4	2	no	—
173	D₁₈₈	—	4	2	no	—
174	D₁₈₈	—	8	2	no	—
175	D₁₈₈	—	8	2	no	—
176	D₁₈₈	—	8	2	no	—
177	D₁₈₈	—	8	2	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	—	2	2	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	C₂×#1701	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	8	4	no	—
188	C₂²×C₄₇	#463	1	2	yes	—
189	C₂²×C₄₇	#469	1	2	yes	—
190	C₂²×C₄₇	#471	1	2	yes	—
191	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
192	C₂×D₄₇	—	8	2	no	—
193	C₂×D₄₇	—	8	2	no	—
194	C₂×D₄₇	—	8	2	no	—
195	C₂×D₄₇	—	16	4	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	—	8	2	no	—
200	C₄×C₄₇	#463	1	2	yes	—
201	C₄×C₄₇	#469	1	2	yes	—
202	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
203	C₄×C₄₇	C₂×AGL(1,ℤ/8)	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	C₂×#486	—	47	1	no	—
207	C₂×#461	D₄₇	1	1	yes	characteristic, complemented
208	C₂×#459	—	47	1	no	—
209	C₂×#436	—	47	1	no	—
210	#1701	—	47	8	no	—
211	C₂×#334	—	47	1	no	—
212	C₂×#332	—	47	1	no	—
213	C₂×#331	—	47	1	no	—
214	C₂×C₄₇	—	8	2	no	—
215	C₂×C₄₇	#1701	1	4	yes	complemented
216	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#469	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
219	D₄₇	—	16	2	no	—
220	C₂²×SD₁₆	—	2	1	no	—
221	C₂²×D₈	—	94	1	no	—
222	C₂²×M₁₆	—	94	1	no	—
223	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×#127	—	47	1	no	—
225	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
226	#486	—	47	4	no	—
227	#486	—	94	2	no	—
228	#461	—	2	2	no	—
229	#461	C₂×D₄₇	1	4	yes	complemented
230	#459	—	47	4	no	—
231	#459	—	94	2	no	—
232	#436	—	47	4	no	—
233	#436	—	94	2	no	—
234	C₂×C₄⋊C₈	—	47	1	no	—
235	C₂×C₄⋊C₈	—	47	1	no	—
236	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×#103	—	2	1	no	—
238	C₂×#102	—	94	1	no	—
239	C₂×#102	—	94	1	no	—
240	C₂×#102	—	94	1	no	—
241	C₂×C₂²⋊C₈	—	94	1	no	—
242	C₂×C₄×C₈	—	47	1	no	—
243	#334	—	47	4	no	—
244	#332	—	47	4	no	—
245	#331	—	47	4	no	—
246	C₄₇	C₂×#1701	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	94	1	no	—
249	C₂²×D₄	—	94	1	no	—
250	C₂²×D₄	—	94	1	no	—
251	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂×SD₁₆	—	2	4	no	—
254	C₂×SD₁₆	—	4	4	no	—
255	C₂×D₈	—	94	4	no	—
256	C₂×D₈	—	188	4	no	—
257	C₂×M₁₆	—	94	4	no	—
258	C₂×M₁₆	—	188	4	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	47	1	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₂²×C₈	—	94	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
268	#127	—	47	2	no	—
269	#127	—	94	1	no	—
270	#127	—	94	1	no	—
271	#127	—	94	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
275	C₄×D₄	C₂²×D₄₇	1	2	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	47	2	no	—
283	C₄⋊C₈	—	47	2	no	—
284	C₄⋊C₈	—	94	1	no	—
285	C₄⋊C₈	—	94	1	no	—
286	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
287	#103	—	2	4	no	—
288	#102	—	94	4	no	—
289	#102	—	94	4	no	—
290	#102	—	94	4	no	—
291	C₂²⋊C₈	—	94	4	no	—
292	C₄×C₈	—	47	2	no	—
293	C₄×C₈	—	47	2	no	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	188	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	94	2	no	—
304	C₂×D₄	—	94	2	no	—
305	C₂×D₄	—	94	2	no	—
306	C₂×D₄	—	376	2	no	—
307	C₂×D₄	—	188	1	no	—
308	C₂×D₄	—	188	1	no	—
309	C₂×D₄	—	188	1	no	—
310	C₂×D₄	—	188	2	no	—
311	C₂×D₄	—	188	2	no	—
312	C₂×D₄	—	188	2	no	—
313	C₂×D₄	—	188	2	no	—
314	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	#10625352	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	SD₁₆	—	4	8	no	—
325	D₈	—	188	8	no	—
326	M₁₆	—	188	8	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	47	2	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	188	2	no	—
336	C₂×C₈	—	188	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₄²	D₄×D₄₇	1	1	yes	characteristic
346	C₄²	#10625352	1	1	yes	characteristic
347	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
348	C₄²	C₂³×D₄₇	1	1	yes	characteristic
349	C₂³	—	2	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	376	2	no	—
354	C₂³	—	376	2	no	—
355	C₂³	—	376	2	no	—
356	C₂³	—	188	2	no	—
357	C₂³	#13093996	1	1	yes	characteristic
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	376	2	no	—
365	D₄	—	376	2	no	—
366	D₄	—	376	2	no	—
367	D₄	—	376	2	no	—
368	D₄	—	188	2	no	—
369	D₄	—	188	2	no	—
370	D₄	—	188	2	no	—
371	D₄	—	188	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	#13093996	1	1	yes	characteristic
381	C₂×C₄	#13093996	1	1	yes	characteristic
382	C₂×C₄	#13093996	1	1	yes	characteristic
383	C₂×C₄	#13094045	1	2	yes	—
384	C₂×C₄	#13094049	1	2	yes	—
385	C₂×C₄	#13094050	1	2	yes	—
386	C₂×C₄	#13094051	1	2	yes	—
387	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	94	2	no	—
392	C₈	—	94	2	no	—
393	C₈	—	188	2	no	—
394	C₈	—	188	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	376	2	no	—
400	C₂²	—	376	2	no	—
401	C₂²	—	376	2	no	—
402	C₂²	—	752	4	no	—
403	C₂²	#15689340	1	2	yes	—
404	C₂²	#15689374	1	2	yes	—
405	C₂²	#15689388	1	2	yes	—
406	C₂²	C₂×#13093996	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	#15689340	1	2	yes	—
412	C₄	#15689374	1	2	yes	—
413	C₄	C₂×#13094045	1	1	yes	characteristic
414	C₄	C₂×#13094049	1	1	yes	characteristic
415	C₄	C₂×#13094050	1	1	yes	characteristic
416	C₄	C₂×#13094051	1	1	yes	characteristic
417	C₂	—	8	2	no	—
418	C₂	—	752	2	no	—
419	C₂	#20242951	1	4	yes	direct product factor
420	C₂	C₂×#15689340	1	1	yes	characteristic
421	C₂	C₂×#15689374	1	1	yes	characteristic
422	C₂	C₂×#15689388	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#461	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#15689318	C₂
hypercenter	C₂×#461	D₄₇
hypocenter	C₄₇	C₂×#1701
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#461

Complements

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

N	H ≅ G/N	type
1. C₂×#15689471	C₂	semidirect
3. C₂×#15689201	C₂	semidirect
4. #20242951	C₂	direct (N × H)
5. C₂×#15688873	C₂	semidirect
6. C₂×#15688869	C₂	semidirect
7. C₂×#15688866	C₂	semidirect
8. C₂×C₄₇×#461	C₂	semidirect
13. #15689471	C₂²	semidirect
17. #15689201	C₂²	semidirect
25. #15688873	C₂²	semidirect
26. #15688869	C₂²	semidirect
27. #15688866	C₂²	semidirect
32. C₄₇×#461	C₂²	semidirect
207. C₂×#461	D₄₇	semidirect
215. C₂×C₄₇	#1701	semidirect
229. #461	C₂×D₄₇	semidirect
246. C₄₇	C₂×#1701	semidirect
419. C₂	#20242951	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×#15689471	2
C₂×#15689318	2
C₂×#15689201	2
#20242951	2
C₂×#15688873	2
C₂×#15688869	2
C₂×#15688866	2
C₂×C₄₇×#461	2
C₂×#1701	47

Subgroups — C2×#20242951 #26198845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242951 #26198845