Subgroups — C₂×#20242823 #26198569

Order 12032.

842 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×#15689469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689328	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242823	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688870	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	C₂³×C₄₇⋊C₈	—	2	1	no	—
11	C₂×#13094024	C₂²	1	1	yes	characteristic
12	#15689469	—	2	2	no	—
13	#15689469	C₂²	1	4	yes	complemented
14	#15689328	—	2	2	no	—
15	#15689328	C₂²	1	4	yes	complemented
16	D₄×C₄₇⋊C₈	—	2	2	no	—
17	D₄×C₄₇⋊C₈	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×#13093947	—	2	1	no	—
21	C₂×#13093945	—	2	1	no	—
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	#15688870	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	—	4	4	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	4	no	—
41	C₂²×C₄₇⋊C₈	—	4	4	no	—
42	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
44	#13094024	—	2	1	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
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	#13093947	—	2	4	no	—
55	#13093945	—	2	4	no	—
56	#13093945	—	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×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂×D₈×C₄₇	—	2	4	no	—
66	C₂×D₈×C₄₇	—	4	4	no	—
67	C₂²×C₈×C₄₇	—	2	1	no	—
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	—	2	1	no	—
71	#127×C₄₇	C₂³	1	2	yes	—
72	C₄×D₄×C₄₇	—	2	1	no	—
73	C₄×D₄×C₄₇	—	2	1	no	—
74	C₄×D₄×C₄₇	D₄	1	2	yes	—
75	C₄×D₄×C₄₇	C₂³	1	2	yes	—
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	#102×C₄₇	—	2	4	no	—
82	C₂⁴×C₄₇	—	2	1	no	—
83	C₂⁴×C₄₇	—	4	1	no	—
84	C₂×D₄×C₄₇	—	2	1	no	—
85	C₂×D₄×C₄₇	—	2	2	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	—	4	1	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	8	2	no	—
97	C₂×D₄×C₄₇	D₈	1	4	yes	—
98	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂²×Dic₄₇	—	4	1	no	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	4	2	no	—
110	C₂×Dic₉₄	—	4	2	no	—
111	C₂×Dic₉₄	—	4	1	no	—
112	D₈×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	C₂×D₄	1	2	yes	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	#41	1	1	yes	characteristic
122	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
123	#10625335	—	4	8	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	4	1	no	—
127	C₄⋊Dic₄₇	—	4	1	no	—
128	C₂×C₄₇⋊C₈	—	2	2	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	—	4	8	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	—	2	4	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	8	2	no	—
143	C₂³×C₄₇	—	8	2	no	—
144	C₂³×C₄₇	—	8	2	no	—
145	C₂³×C₄₇	#121	1	1	yes	characteristic
146	D₄×C₄₇	—	2	2	no	—
147	D₄×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	4	2	no	—
152	D₄×C₄₇	—	8	2	no	—
153	D₄×C₄₇	—	8	2	no	—
154	D₄×C₄₇	—	8	2	no	—
155	D₄×C₄₇	—	8	2	no	—
156	D₄×C₄₇	C₂×D₈	1	4	yes	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₄₇	#135	1	2	yes	—
168	C₂×C₄×C₄₇	#135	1	2	yes	—
169	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	8	2	no	—
175	Dic₉₄	—	4	2	no	—
176	Dic₉₄	—	4	2	no	—
177	Dic₉₄	—	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×#1681	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	4	8	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	16	4	no	—
192	C₂²×C₄₇	#463	1	2	yes	—
193	C₂²×C₄₇	#466	1	2	yes	—
194	C₂²×C₄₇	#471	1	2	yes	—
195	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	#463	1	2	yes	—
200	C₄×C₄₇	#466	1	2	yes	—
201	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
205	Dic₄₇	—	8	2	no	—
206	C₂×#486	—	47	1	no	—
207	C₂×#461	—	47	1	no	—
208	C₂×#459	D₄₇	1	1	yes	characteristic
209	C₂×C₈×D₄	—	47	1	no	—
210	#1681	—	47	8	no	—
211	C₂×#335	—	47	1	no	—
212	C₂×#332	—	47	1	no	—
213	C₂×#331	—	47	1	no	—
214	C₂×C₄₇	—	4	4	no	—
215	C₂×C₄₇	—	16	2	no	—
216	C₂×C₄₇	#1681	1	4	yes	complemented
217	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#466	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
220	C₂²×SD₁₆	—	94	1	no	—
221	C₂²×D₈	—	2	1	no	—
222	C₂³×C₈	—	94	1	no	—
223	C₂×C₄⋊Q₈	—	47	1	no	—
224	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
226	#486	—	47	4	no	—
227	#486	—	94	2	no	—
228	#461	—	47	4	no	—
229	#461	—	94	2	no	—
230	#459	—	2	2	no	—
231	#459	C₂×D₄₇	1	4	yes	—
232	C₈×D₄	—	47	4	no	—
233	C₈×D₄	—	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	—	94	1	no	—
238	C₂×#102	—	2	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	#335	—	47	4	no	—
244	#332	—	47	4	no	—
245	#331	—	47	4	no	—
246	C₄₇	C₂×#1681	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	94	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂×SD₁₆	—	94	4	no	—
254	C₂×SD₁₆	—	188	4	no	—
255	C₂×D₈	—	2	4	no	—
256	C₂×D₈	—	4	4	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	—	94	4	no	—
261	C₂²×C₈	—	94	1	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₂²×C₈	—	188	4	no	—
264	C₄⋊Q₈	—	47	2	no	—
265	C₄⋊Q₈	—	94	1	no	—
266	C₄⋊Q₈	—	94	1	no	—
267	C₄⋊Q₈	—	94	1	no	—
268	#127	—	2	1	no	—
269	#127	—	2	1	no	—
270	#127	—	2	1	no	—
271	#127	C₂²×D₄₇	1	2	yes	—
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	—	94	1	no	—
277	C₂×C₄⋊C₄	—	94	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	—	94	4	no	—
288	#102	—	2	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	—	4	1	no	—
296	C₂×Q₈	—	94	2	no	—
297	C₂×Q₈	—	188	2	no	—
298	C₂×Q₈	—	188	2	no	—
299	C₂×Q₈	—	188	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	#10625334	1	4	yes	—
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	—	188	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	—	188	8	no	—
325	D₈	—	4	8	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	47	2	no	—
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₂×C₈	—	188	8	no	—
335	C₂×C₈	—	188	2	no	—
336	C₂×C₈	—	188	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	94	2	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	188	1	no	—
341	C₄⋊C₄	—	188	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	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	#13093996	1	1	yes	characteristic
358	Q₈	—	376	2	no	—
359	Q₈	—	188	2	no	—
360	Q₈	—	188	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	C₂×#10625334	1	4	yes	—
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	—	376	2	no	—
379	C₂×C₄	—	188	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	C₂×#10625334	1	2	yes	—
384	C₂×C₄	#13094043	1	2	yes	—
385	C₂×C₄	#13094044	1	2	yes	—
386	C₂×C₄	#13094048	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	—	2	4	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	16	4	no	—
403	C₂²	#15689336	1	2	yes	—
404	C₂²	#15689357	1	2	yes	—
405	C₂²	#15689384	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	—	376	2	no	—
411	C₄	#15689336	1	2	yes	—
412	C₄	#15689357	1	2	yes	—
413	C₄	C₂²×#10625334	1	1	yes	characteristic
414	C₄	C₂×#13094043	1	1	yes	characteristic
415	C₄	C₂×#13094044	1	1	yes	characteristic
416	C₄	C₂×#13094048	1	1	yes	characteristic
417	C₂	—	4	4	no	—
418	C₂	—	16	2	no	—
419	C₂	#20242823	1	4	yes	direct product factor
420	C₂	C₂×#15689336	1	1	yes	characteristic
421	C₂	C₂×#15689357	1	1	yes	characteristic
422	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×#1681
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×#15689469	C₂	semidirect
2. C₂×#15689328	C₂	semidirect
3. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
4. #20242823	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
6. C₂×#15688870	C₂	semidirect
7. C₂×#15688867	C₂	semidirect
13. #15689469	C₂²	semidirect
15. #15689328	C₂²	semidirect
17. D₄×C₄₇⋊C₈	C₂²	semidirect
25. #15688875	C₂²	semidirect
26. #15688870	C₂²	semidirect
27. #15688867	C₂²	semidirect
216. C₂×C₄₇	#1681	semidirect
246. C₄₇	C₂×#1681	semidirect
419. C₂	#20242823	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×#15689469	2
C₂×#15689328	2
C₂×D₄×C₄₇⋊C₈	2
#20242823	2
C₂×#15688875	2
C₂×#15688870	2
C₂×#15688867	2
C₂×C₄₇×#459	2
C₂×#1681	47

Subgroups — C2×#20242823 #26198569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242823 #26198569