Subgroups — C₂×#20242850 #26198768

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×#15689400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689315	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689202	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242850	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625334	—	2	1	no	—
10	C₂²×#10625324	—	2	1	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	#15689400	—	2	2	no	—
13	#15689400	C₂²	1	4	yes	complemented
14	#15689315	—	2	2	no	—
15	#15689315	C₂²	1	4	yes	—
16	#15689202	—	2	2	no	—
17	#15689202	C₂²	1	4	yes	complemented
18	C₂×#13093957	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
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×#13093944	—	2	1	no	—
24	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
25	#15688876	C₂²	1	4	yes	complemented
26	#15688869	C₂²	1	4	yes	complemented
27	#15688867	C₂²	1	4	yes	complemented
28	C₂²×SD₁₆×C₄₇	—	2	1	no	—
29	C₂²×SD₁₆×C₄₇	—	2	1	no	—
30	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#492	—	2	2	no	—
33	C₄₇×#492	C₂²	1	4	yes	complemented
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₇	—	2	1	no	—
37	C₂×#10625334	—	2	4	no	—
38	C₂×#10625334	—	4	4	no	—
39	C₂×#10625324	—	2	4	no	—
40	C₂×#10625324	—	4	4	no	—
41	C₂²×C₄₇⋊C₈	—	2	1	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₄×D₁₈₈	—	2	1	no	—
45	C₄×D₁₈₈	—	2	1	no	—
46	C₄×D₁₈₈	D₄	1	2	yes	—
47	C₄×D₁₈₈	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
50	#13093957	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093945	—	2	4	no	—
58	#13093944	—	2	4	no	—
59	(C₂×D₄₇)⋊C₈	—	2	4	no	—
60	C₂²×Q₈×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂×SD₁₆×C₄₇	—	2	4	no	—
65	C₂×SD₁₆×C₄₇	—	2	4	no	—
66	C₂×SD₁₆×C₄₇	—	4	4	no	—
67	C₂×SD₁₆×C₄₇	—	4	4	no	—
68	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
74	#127×C₄₇	—	2	1	no	—
75	#127×C₄₇	—	2	1	no	—
76	#127×C₄₇	—	2	1	no	—
77	#127×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₄₇	D₄	1	2	yes	—
82	C₄×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂⁴×C₄₇	—	4	1	no	—
84	C₂³×D₄₇	—	2	1	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	4	1	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×Q₈×C₄₇	—	4	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	1	no	—
94	C₂×D₄×C₄₇	—	4	1	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	—	4	2	no	—
99	C₂×D₄×C₄₇	—	8	2	no	—
100	C₂²×C₄×C₄₇	—	4	1	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×Dic₄₇	—	2	1	no	—
105	C₂×D₁₈₈	—	2	2	no	—
106	C₂×D₁₈₈	—	2	2	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	—	4	2	no	—
112	C₂×C₄×D₄₇	—	4	2	no	—
113	SD₁₆×C₄₇	—	4	8	no	—
114	SD₁₆×C₄₇	—	4	8	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	D₈	1	4	yes	complemented
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	4	1	no	—
122	C₄⋊C₄×C₄₇	—	4	1	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	(C₂×D₄₇)⋊C₄	—	2	2	no	—
129	(C₂×D₄₇)⋊C₄	—	2	2	no	—
130	C₄⋊Dic₄₇	—	2	1	no	—
131	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	4	2	no	—
136	C₂×C₄₇⋊C₈	—	4	2	no	—
137	C₂×C₄₇⋊C₈	—	4	2	no	—
138	#10625324	—	4	8	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	8	2	no	—
141	C₂³×C₄₇	—	8	2	no	—
142	C₂³×C₄₇	—	8	2	no	—
143	C₂³×C₄₇	#121	1	1	yes	characteristic
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	4	2	no	—
146	C₂²×D₄₇	—	4	2	no	—
147	C₂²×D₄₇	—	4	2	no	—
148	Q₈×C₄₇	—	4	2	no	—
149	Q₈×C₄₇	—	4	2	no	—
150	Q₈×C₄₇	—	8	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	—	4	2	no	—
161	C₂×C₄×C₄₇	—	8	2	no	—
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₄₇	#137	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	D₁₈₈	—	2	2	no	—
175	D₁₈₈	—	2	2	no	—
176	D₁₈₈	—	4	2	no	—
177	C₄×D₄₇	—	4	2	no	—
178	C₄×D₄₇	—	4	2	no	—
179	C₄×D₄₇	—	4	4	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	C₂×D₈	1	4	yes	complemented
182	C₄₇⋊C₈	—	4	2	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	C₂×#1685	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	16	4	no	—
190	C₂²×C₄₇	#459	1	2	yes	—
191	C₂²×C₄₇	#468	1	2	yes	—
192	C₂²×C₄₇	#471	1	2	yes	—
193	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
194	C₂×D₄₇	—	4	2	no	—
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₂×D₄₇	—	8	4	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	8	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	—	4	2	no	—
208	C₂×#492	D₄₇	1	1	yes	characteristic, complemented
209	C₂×#474	—	47	1	no	—
210	C₂×#459	—	47	1	no	—
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	—	16	2	no	—
217	C₂×C₄₇	#1685	1	4	yes	complemented
218	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
221	D₄₇	—	8	2	no	—
222	C₂²×SD₁₆	—	2	1	no	—
223	C₂²×SD₁₆	—	2	1	no	—
224	C₂²×D₈	—	94	1	no	—
225	C₂²×M₁₆	—	94	1	no	—
226	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
228	C₂×C₄×D₄	—	47	1	no	—
229	#492	—	2	2	no	—
230	#492	C₂×D₄₇	1	4	yes	complemented
231	#474	—	47	4	no	—
232	#474	—	94	2	no	—
233	#459	—	47	4	no	—
234	#459	—	94	2	no	—
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	—	47	1	no	—
241	C₂×#102	—	94	1	no	—
242	C₂×#102	—	94	1	no	—
243	C₂×C₂²⋊C₈	—	94	1	no	—
244	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	—	47	1	no	—
254	C₂³×C₄	—	94	1	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	4	4	no	—
258	C₂×SD₁₆	—	4	4	no	—
259	C₂×D₈	—	94	4	no	—
260	C₂×D₈	—	188	4	no	—
261	C₂×M₁₆	—	94	4	no	—
262	C₂×M₁₆	—	188	4	no	—
263	C₂²×C₈	—	94	1	no	—
264	C₂²×C₈	—	94	1	no	—
265	C₂²×C₈	—	94	1	no	—
266	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
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	—	47	2	no	—
277	C₄×D₄	—	47	2	no	—
278	C₄×D₄	—	94	1	no	—
279	C₄×D₄	—	94	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	47	1	no	—
283	C₂×C₂²⋊C₄	—	94	1	no	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	#107	—	94	4	no	—
286	C₄⋊C₈	—	47	2	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	—	94	1	no	—
292	#102	—	94	4	no	—
293	#102	—	94	4	no	—
294	C₂²⋊C₈	—	94	4	no	—
295	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
296	C₄×C₈	C₂²×D₄₇	1	2	yes	—
297	C₂⁴	—	4	1	no	—
298	C₂⁴	—	94	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	94	1	no	—
316	C₂×D₄	—	94	2	no	—
317	C₂×D₄	—	94	2	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	—	94	2	no	—
322	C₂²×C₄	—	188	2	no	—
323	C₂²×C₄	—	188	2	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	—	4	8	no	—
328	SD₁₆	—	4	8	no	—
329	D₈	—	188	8	no	—
330	M₁₆	—	188	8	no	—
331	C₂×C₈	—	2	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	C₂×C₈	—	188	2	no	—
338	C₂×C₈	#10625334	1	4	yes	complemented
339	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₂²⋊C₄	—	94	2	no	—
348	C₂²⋊C₄	—	94	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	—	4	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	—	8	2	no	—
356	C₂³	—	8	2	no	—
357	C₂³	—	94	2	no	—
358	C₂³	—	188	2	no	—
359	C₂³	—	188	2	no	—
360	C₂³	—	188	2	no	—
361	C₂³	#13093995	1	1	yes	characteristic
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	94	2	no	—
374	D₄	—	94	2	no	—
375	D₄	—	188	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	4	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	#13093995	1	1	yes	characteristic
385	C₂×C₄	#13093995	1	1	yes	characteristic
386	C₂×C₄	#13093995	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625334	1	2	yes	—
388	C₂×C₄	#13094050	1	2	yes	—
389	C₂×C₄	#13094051	1	2	yes	—
390	C₂×C₄	#13094053	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	—	2	2	no	—
395	C₈	—	188	2	no	—
396	C₈	—	188	2	no	—
397	C₈	—	188	2	no	—
398	C₈	C₂×#10625334	1	4	yes	complemented
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	16	4	no	—
403	C₂²	—	376	4	no	—
404	C₂²	—	188	2	no	—
405	C₂²	—	188	2	no	—
406	C₂²	—	188	2	no	—
407	C₂²	#15689315	1	2	yes	—
408	C₂²	#15689366	1	2	yes	—
409	C₂²	#15689383	1	2	yes	—
410	C₂²	C₂×#13093995	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	188	2	no	—
415	C₄	#15689315	1	2	yes	—
416	C₄	#15689366	1	2	yes	—
417	C₄	C₂²×#10625334	1	1	yes	characteristic
418	C₄	C₂×#13094050	1	1	yes	characteristic
419	C₄	C₂×#13094051	1	1	yes	characteristic
420	C₄	C₂×#13094053	1	1	yes	characteristic
421	C₂	—	16	2	no	—
422	C₂	—	376	2	no	—
423	C₂	#20242850	1	4	yes	direct product factor
424	C₂	C₂×#15689315	1	1	yes	characteristic
425	C₂	C₂×#15689366	1	1	yes	characteristic
426	C₂	C₂×#15689383	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#492	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#15689315	C₂
hypercenter	C₂×#492	D₄₇
hypocenter	C₄₇	C₂×#1685
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. C₂×#15689400	C₂	semidirect
3. C₂×#15689202	C₂	semidirect
4. #20242850	C₂	direct (N × H)
5. C₂×#15688876	C₂	semidirect
6. C₂×#15688869	C₂	semidirect
7. C₂×#15688867	C₂	semidirect
8. C₂×C₄₇×#492	C₂	semidirect
13. #15689400	C₂²	semidirect
17. #15689202	C₂²	semidirect
25. #15688876	C₂²	semidirect
26. #15688869	C₂²	semidirect
27. #15688867	C₂²	semidirect
33. C₄₇×#492	C₂²	semidirect
116. C₂×C₈×C₄₇	D₈	semidirect
181. C₈×C₄₇	C₂×D₈	semidirect
208. C₂×#492	D₄₇	semidirect
217. C₂×C₄₇	#1685	semidirect
230. #492	C₂×D₄₇	semidirect
248. C₄₇	C₂×#1685	semidirect
338. C₂×C₈	#10625334	semidirect
398. C₈	C₂×#10625334	semidirect
423. C₂	#20242850	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×#15689400	2
C₂×#15689315	2
C₂×#15689202	2
#20242850	2
C₂×#15688876	2
C₂×#15688869	2
C₂×#15688867	2
C₂×C₄₇×#492	2
C₂×#1685	47

Subgroups — C2×#20242850 #26198768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242850 #26198768