Subgroups — C₂×#20252299 #27080592

Order 12032.

2674 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689923	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689889	C₂	1	2	yes	maximal, complemented
3	#20252299	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689246	C₂	1	4	yes	maximal, complemented
5	C₂×#15689241	C₂	1	4	yes	maximal, complemented
6	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093952	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	2	yes	—
10	#15689923	C₄	1	8	yes	complemented
11	#15689923	C₂²	1	8	yes	—
12	C₂×#13094057	C₄	1	4	yes	complemented
13	C₂×#13094052	C₄	1	4	yes	complemented
14	C₂×#13094046	C₂²	1	4	yes	—
15	#15689889	—	2	8	no	—
16	#15689889	C₂²	1	16	yes	complemented
17	C₂×#13094032	—	2	4	no	—
18	C₂×#13094030	C₂²	1	8	yes	complemented
19	C₂²×#10625329	C₂²	1	2	yes	—
20	C₂×M₁₆×D₄₇	—	2	4	no	—
21	#15689246	C₂²	1	32	yes	complemented
22	#15689241	C₂²	1	32	yes	complemented
23	#15689172	C₂²	1	8	yes	complemented
24	C₂×#13093960	C₂²	1	4	yes	complemented
25	C₂×#13093952	C₂²	1	4	yes	complemented
26	C₂×#13093952	C₂²	1	4	yes	complemented
27	C₂×#13093952	C₂²	1	16	yes	complemented
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₄₇	C₂²	1	8	yes	complemented
32	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
33	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
34	C₂×#10625350	—	2	2	no	—
35	C₂×#10625350	—	2	4	no	—
36	C₂×#10625350	—	2	2	no	—
37	C₂×#10625350	—	2	4	no	—
38	C₂×#10625350	C₂×C₄	1	4	yes	—
39	C₂×#10625350	C₂×C₄	1	8	yes	—
40	C₂×#10625350	C₂³	1	4	yes	—
41	C₂×#10625350	C₂³	1	8	yes	—
42	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
44	C₂²×C₂²⋊D₄₇	—	2	2	no	—
45	C₂²×C₄×D₄₇	—	2	2	no	—
46	#13094057	C₂×C₄	1	32	yes	complemented
47	#13094052	C₂×C₄	1	32	yes	complemented
48	#13094046	C₂×C₄	1	16	yes	complemented
49	#13094046	C₂³	1	16	yes	—
50	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	complemented
51	C₂×#10625325	C₂×C₄	1	8	yes	complemented
52	C₂×D₃₇₆	C₂×C₄	1	4	yes	complemented
53	#13094032	—	2	32	no	—
54	#13094030	—	2	16	no	—
55	#13094030	C₂³	1	32	yes	complemented
56	C₂×#10625329	—	2	2	no	—
57	C₂×#10625329	—	2	4	no	—
58	C₂×#10625329	C₂³	1	4	yes	—
59	C₂×#10625329	C₂³	1	8	yes	—
60	C₂×#10625324	—	2	8	no	—
61	M₁₆×D₄₇	—	2	32	no	—
62	C₂²×C₄₇⋊C₈	—	2	2	no	—
63	C₂×C₈×D₄₇	—	2	8	no	—
64	#13093960	C₂³	1	16	yes	complemented
65	#13093952	C₂³	1	16	yes	complemented
66	#13093952	C₂³	1	16	yes	complemented
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
72	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
73	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
74	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
82	#97×C₄₇	C₂³	1	8	yes	complemented
83	C₄×C₈×C₄₇	C₂³	1	8	yes	complemented
84	C₂⁴×C₄₇	#41	1	1	yes	characteristic
85	C₂³×D₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
98	C₂×C₂²⋊D₄₇	—	2	4	no	—
99	C₂×C₂²⋊D₄₇	—	2	8	no	—
100	C₂×C₂²⋊D₄₇	—	2	4	no	—
101	C₂×C₂²⋊D₄₇	—	2	8	no	—
102	C₂²×Dic₄₇	—	2	2	no	—
103	#10625350	—	2	8	no	—
104	#10625350	—	2	8	no	—
105	#10625350	—	2	8	no	—
106	#10625350	—	2	4	no	—
107	#10625350	—	2	8	no	—
108	#10625350	—	2	4	no	—
109	#10625350	—	2	8	no	—
110	#10625350	C₂²×C₄	1	8	yes	—
111	#10625350	C₂²×C₄	1	16	yes	—
112	#10625350	C₂⁴	1	8	yes	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	4	no	—
115	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
116	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
117	C₂×C₄×D₄₇	—	2	4	no	—
118	C₂×C₄×D₄₇	—	2	8	no	—
119	C₂×C₄×D₄₇	—	2	4	no	—
120	C₂×C₄×D₄₇	—	2	8	no	—
121	C₂×Dic₉₄	—	2	2	no	—
122	C₂×Dic₉₄	—	2	4	no	—
123	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
124	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
125	M₁₆×C₄₇	C₂²×C₄	1	16	yes	—
126	M₁₆×C₄₇	C₂×D₄	1	16	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
132	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	4	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	C₂⁴	1	2	yes	—
137	C₄²×C₄₇	C₂⁴	1	2	yes	—
138	#10625329	—	2	8	no	—
139	#10625329	—	2	4	no	—
140	#10625329	C₂⁴	1	8	yes	—
141	C₂×C₄₇⋊C₈	—	2	4	no	—
142	C₂×C₄₇⋊C₈	—	2	8	no	—
143	Dic₁₈₈	C₂²×C₄	1	16	yes	complemented
144	D₃₇₆	C₂²×C₄	1	16	yes	complemented
145	#10625325	C₂²×C₄	1	32	yes	complemented
146	#10625324	—	2	32	no	—
147	C₈×D₄₇	—	2	32	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	C₄×D₄	1	2	yes	—
150	C₂³×C₄₇	C₄×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×#41	1	2	yes	—
153	C₂²×D₄₇	—	2	4	no	—
154	C₂²×D₄₇	—	2	8	no	—
155	C₂²×D₄₇	—	8	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	8	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	4	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×C₄×C₄₇	C₂×#41	1	2	yes	—
173	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
174	C₂²⋊D₄₇	—	2	16	no	—
175	C₂²⋊D₄₇	—	2	8	no	—
176	C₂²⋊D₄₇	—	2	8	no	—
177	C₂×Dic₄₇	—	2	8	no	—
178	C₂×Dic₄₇	—	2	4	no	—
179	D₁₈₈	—	2	4	no	—
180	D₁₈₈	—	2	8	no	—
181	D₁₈₈	C₂³×C₄	1	8	yes	—
182	C₄×D₄₇	—	2	16	no	—
183	C₄×D₄₇	—	2	8	no	—
184	C₄×D₄₇	—	2	8	no	—
185	Dic₉₄	—	2	4	no	—
186	Dic₉₄	—	2	8	no	—
187	Dic₉₄	C₂³×C₄	1	8	yes	—
188	C₈×C₄₇	C₂³×C₄	1	8	yes	—
189	C₈×C₄₇	C₂²×D₄	1	8	yes	—
190	C₄₇⋊C₈	—	2	8	no	—
191	C₂×#2956	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
200	C₂×D₄₇	—	2	8	no	—
201	C₂×D₄₇	—	4	8	no	—
202	C₂×D₄₇	—	8	8	no	—
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
207	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
209	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
210	Dic₄₇	—	2	8	no	—
211	C₂×#575	—	47	1	no	—
212	C₂×#568	—	47	2	no	—
213	#2956	—	47	16	no	—
214	C₂×#444	—	47	4	no	—
215	C₂×#443	—	47	4	no	—
216	C₂×#430	—	47	1	no	—
217	C₂²×#104	—	47	2	no	—
218	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic, complemented
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	2	4	no	—
221	C₂×C₄₇	—	2	1	no	—
222	C₂×C₄₇	#2956	1	2	yes	complemented
223	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
224	D₄₇	—	4	8	no	—
225	C₂²×#41	—	47	2	no	—
226	#575	—	47	8	no	—
227	#575	—	47	8	no	—
228	C₂×#137	—	47	4	no	—
229	C₂×AGL(1,ℤ/8)	—	47	4	no	—
230	C₂×#135	—	47	4	no	—
231	#568	—	47	16	no	—
232	#568	—	94	8	no	—
233	C₂×#131	—	47	8	no	—
234	C₂×#131	—	94	4	no	—
235	C₂²×M₁₆	—	47	2	no	—
236	C₂²×M₁₆	—	94	4	no	—
237	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
238	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
239	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
240	#444	—	47	32	no	—
241	#443	—	47	32	no	—
242	#430	—	47	8	no	—
243	C₂×#108	—	47	4	no	—
244	C₂×#104	—	47	4	no	—
245	C₂×#104	—	47	4	no	—
246	C₂×#104	—	47	16	no	—
247	C₄×M₁₆	C₂×D₄₇	1	8	yes	complemented
248	C₂×#97	C₂×D₄₇	1	2	yes	complemented
249	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	complemented
250	C₄₇	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
251	C₂×#41	—	47	4	no	—
252	C₂×#41	—	47	8	no	—
253	C₂×#41	—	47	4	no	—
254	C₂×#41	—	47	8	no	—
255	C₂×#41	—	94	2	no	—
256	C₂×#41	—	94	4	no	—
257	C₂×#41	—	94	2	no	—
258	C₂×#41	—	94	4	no	—
259	C₂²×Q₈	—	47	2	no	—
260	C₂²×D₄	—	47	2	no	—
261	C₂²×D₄	—	94	2	no	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	—	94	2	no	—
264	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
265	#137	—	47	32	no	—
266	AGL(1,ℤ/8)	—	47	32	no	—
267	#135	—	47	16	no	—
268	#135	—	47	16	no	—
269	C₂×Q₁₆	—	47	4	no	—
270	C₂×SD₁₆	—	47	8	no	—
271	C₂×D₈	—	47	4	no	—
272	#131	—	47	32	no	—
273	#131	—	94	32	no	—
274	#131	—	94	16	no	—
275	C₂×M₁₆	—	47	4	no	—
276	C₂×M₁₆	—	47	8	no	—
277	C₂×M₁₆	—	94	2	no	—
278	C₂×M₁₆	—	94	4	no	—
279	C₂×M₁₆	—	94	32	no	—
280	C₂×M₁₆	—	94	8	no	—
281	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
282	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
283	C₂×M₁₆	D₁₈₈	1	4	yes	—
284	C₂×M₁₆	D₁₈₈	1	4	yes	—
285	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
286	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
287	C₂²×C₈	—	94	2	no	—
288	C₂²×C₈	—	94	8	no	—
289	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
290	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
296	#108	—	47	16	no	—
297	#104	—	47	16	no	—
298	#104	—	47	16	no	—
299	#97	C₂²×D₄₇	1	8	yes	complemented
300	C₄×C₈	C₂²×D₄₇	1	8	yes	complemented
301	C₂⁴	—	94	2	no	—
302	C₂⁴	#10625350	1	1	yes	characteristic
303	#41	—	47	8	no	—
304	#41	—	47	16	no	—
305	#41	—	47	8	no	—
306	#41	—	94	8	no	—
307	#41	—	94	8	no	—
308	#41	—	94	8	no	—
309	#41	—	94	8	no	—
310	#41	—	94	4	no	—
311	#41	—	94	4	no	—
312	#41	—	94	8	no	—
313	C₂×Q₈	—	47	4	no	—
314	C₂×Q₈	—	47	8	no	—
315	C₂×Q₈	—	94	2	no	—
316	C₂×Q₈	—	94	4	no	—
317	C₂×D₄	—	47	4	no	—
318	C₂×D₄	—	47	8	no	—
319	C₂×D₄	—	94	8	no	—
320	C₂×D₄	—	94	4	no	—
321	C₂×D₄	—	94	8	no	—
322	C₂×D₄	—	94	4	no	—
323	C₂×D₄	—	94	2	no	—
324	C₂×D₄	—	94	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	—	94	4	no	—
331	C₂²×C₄	—	94	8	no	—
332	C₂²×C₄	—	94	8	no	—
333	C₂²×C₄	—	94	4	no	—
334	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
335	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
336	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
337	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
338	C₂²×C₄	#10625350	1	1	yes	characteristic
339	C₂²×C₄	#10625350	1	2	yes	—
340	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
341	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
342	Q₁₆	—	47	16	no	—
343	SD₁₆	—	47	32	no	—
344	D₈	—	47	16	no	—
345	M₁₆	—	47	8	no	—
346	M₁₆	—	94	8	no	—
347	M₁₆	—	94	4	no	—
348	M₁₆	—	94	32	no	—
349	M₁₆	C₂×C₄×D₄₇	1	16	yes	—
350	M₁₆	C₂×D₁₈₈	1	16	yes	—
351	C₂×C₈	—	94	8	no	—
352	C₂×C₈	—	94	4	no	—
353	C₂×C₈	—	94	32	no	—
354	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
355	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
356	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
357	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
358	C₂×C₈	C₂³×D₄₇	1	4	yes	—
359	C₂×C₈	C₂³×D₄₇	1	4	yes	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	4	no	—
362	C₄²	—	2	1	no	—
363	C₄²	C₂³×D₄₇	1	2	yes	—
364	C₄²	C₂³×D₄₇	1	2	yes	—
365	C₂³	—	4	2	no	—
366	C₂³	—	94	8	no	—
367	C₂³	—	94	4	no	—
368	C₂³	—	376	4	no	—
369	C₂³	C₄×D₁₈₈	1	2	yes	—
370	C₂³	C₄×D₁₈₈	1	2	yes	—
371	C₂³	C₂×#10625350	1	1	yes	characteristic
372	C₂³	C₂×#10625350	1	2	yes	—
373	Q₈	—	47	8	no	—
374	Q₈	—	94	8	no	—
375	Q₈	—	94	4	no	—
376	D₄	—	47	8	no	—
377	D₄	—	94	16	no	—
378	D₄	—	94	8	no	—
379	D₄	—	94	8	no	—
380	D₄	—	94	8	no	—
381	D₄	—	94	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	94	8	no	—
388	C₂×C₄	—	94	4	no	—
389	C₂×C₄	—	94	8	no	—
390	C₂×C₄	—	94	16	no	—
391	C₂×C₄	—	94	8	no	—
392	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
393	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
394	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
395	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
399	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
400	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
403	C₂×C₄	C₂×#10625350	1	2	yes	—
404	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
405	C₈	—	94	8	no	—
406	C₈	C₂²×C₄×D₄₇	1	8	yes	—
407	C₈	C₂²×D₁₈₈	1	8	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	94	8	no	—
413	C₂²	—	376	8	no	—
414	C₂²	—	188	8	no	—
415	C₂²	C₂×C₄×D₁₈₈	1	4	yes	—
416	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
417	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
418	C₂²	C₂²×#10625350	1	1	yes	characteristic
419	C₄	—	2	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	94	8	no	—
422	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
423	C₄	C₂×C₄×D₁₈₈	1	4	yes	—
424	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
425	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
426	C₄	C₂³×D₁₈₈	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	188	8	no	—
431	C₂	#20252299	1	2	yes	direct product factor
432	C₂	C₂²×C₄×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#15689923	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₂×#2956
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#15689889	C₂	semidirect
3. #20252299	C₂	direct (N × H)
4. C₂×#15689246	C₂	semidirect
5. C₂×#15689241	C₂	semidirect
6. C₂×#15689172	C₂	semidirect
7. C₂²×#13093952	C₂	semidirect
8. C₂×C₄×M₁₆×C₄₇	C₂	semidirect
10. #15689923	C₄	semidirect
12. C₂×#13094057	C₄	semidirect
13. C₂×#13094052	C₄	semidirect
16. #15689889	C₂²	semidirect
18. C₂×#13094030	C₂²	semidirect
21. #15689246	C₂²	semidirect
22. #15689241	C₂²	semidirect
23. #15689172	C₂²	semidirect
24. C₂×#13093960	C₂²	semidirect
25. C₂×#13093952	C₂²	semidirect
26. C₂×#13093952	C₂²	semidirect
27. C₂×#13093952	C₂²	semidirect
31. C₄×M₁₆×C₄₇	C₂²	semidirect
32. C₂×#97×C₄₇	C₂²	semidirect
33. C₂×C₄×C₈×C₄₇	C₂²	semidirect
46. #13094057	C₂×C₄	semidirect
47. #13094052	C₂×C₄	semidirect
48. #13094046	C₂×C₄	semidirect
50. C₂×Dic₁₈₈	C₂×C₄	semidirect
51. C₂×#10625325	C₂×C₄	semidirect
52. C₂×D₃₇₆	C₂×C₄	semidirect
55. #13094030	C₂³	semidirect
64. #13093960	C₂³	semidirect
65. #13093952	C₂³	semidirect
66. #13093952	C₂³	semidirect
82. #97×C₄₇	C₂³	semidirect
83. C₄×C₈×C₄₇	C₂³	semidirect
143. Dic₁₈₈	C₂²×C₄	semidirect
144. D₃₇₆	C₂²×C₄	semidirect
145. #10625325	C₂²×C₄	semidirect
218. C₂×C₄×M₁₆	D₄₇	semidirect
222. C₂×C₄₇	#2956	semidirect
247. C₄×M₁₆	C₂×D₄₇	semidirect
248. C₂×#97	C₂×D₄₇	semidirect
249. C₂×C₄×C₈	C₂×D₄₇	semidirect
250. C₄₇	C₂×#2956	semidirect
299. #97	C₂²×D₄₇	semidirect
300. C₄×C₈	C₂²×D₄₇	semidirect
431. C₂	#20252299	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×#15689923	2
C₂×#15689889	2
#20252299	2
C₂×#15689246	2
C₂×#15689241	2
C₂×#15689172	2
C₂²×#13093952	2
C₂×C₄×M₁₆×C₄₇	2
C₂×#2956	47

Subgroups — C2×#20252299 #27080592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252299 #27080592