Subgroups — C₂×#20243498 #26216140

Order 12032.

1434 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689597	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093940	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13093940	C₂	1	1	yes	maximal, characteristic
4	#20243498	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	#15689597	—	2	2	no	—
13	#15689597	—	2	2	no	—
14	#15689597	C₄	1	4	yes	—
15	#15689597	C₂²	1	4	yes	—
16	C₂×C₄×D₁₈₈	—	2	2	no	—
17	C₂×#13093986	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×D₄₇	C₄	1	4	yes	—
20	C₂×#13093940	—	2	2	no	—
21	C₂×#13093940	—	2	2	no	—
22	C₂×#13093940	—	2	2	no	—
23	C₂×#13093940	—	2	2	no	—
24	C₂×#13093940	C₂²	1	4	yes	—
25	C₂×#13093940	C₂²	1	4	yes	—
26	#15688895	C₂²	1	4	yes	complemented
27	#15688894	C₂²	1	4	yes	complemented
28	#15688893	C₂²	1	4	yes	complemented
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#344	C₂²	1	4	yes	complemented
33	C₂⁴×D₄₇	C₂×C₄	1	2	yes	—
34	C₂²×D₁₈₈	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	D₄	1	2	yes	—
44	C₂²×D₁₈₈	D₄	1	2	yes	—
45	C₂²×D₁₈₈	D₄	1	2	yes	—
46	C₂²×D₁₈₈	D₄	1	2	yes	—
47	C₂²×D₁₈₈	C₂³	1	2	yes	—
48	C₂²×C₄×D₄₇	—	2	4	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₂×#10625329	C₂³	1	2	yes	—
61	C₂²×C₄₇⋊C₈	—	2	1	no	—
62	C₂²×C₄₇⋊C₈	—	2	1	no	—
63	C₄×D₁₈₈	—	2	8	no	—
64	C₄×D₁₈₈	—	2	8	no	—
65	#13093986	—	2	8	no	—
66	#13093986	—	2	8	no	—
67	#13093983	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093983	C₂×C₄	1	2	yes	—
70	#13093983	C₂³	1	2	yes	—
71	C₂×C₄⋊Dic₄₇	—	2	1	no	—
72	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
73	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
74	C₂²⋊C₄×D₄₇	—	2	8	no	—
75	C₂²⋊C₄×D₄₇	C₂×C₄	1	16	yes	—
76	C₂×C₄×Dic₄₇	—	2	1	no	—
77	#13093940	—	2	8	no	—
78	#13093940	—	2	8	no	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
91	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₄₇	—	2	1	no	—
93	C₂²×C₈×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	#117×C₄₇	—	2	1	no	—
96	#117×C₄₇	C₂×C₄	1	2	yes	—
97	#117×C₄₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂³×D₄₇	—	2	2	no	—
103	C₂³×D₄₇	—	2	2	no	—
104	C₂³×D₄₇	—	2	2	no	—
105	C₂³×D₄₇	—	2	2	no	—
106	C₂³×D₄₇	—	8	4	no	—
107	C₂³×D₄₇	C₂²⋊C₄	1	4	yes	—
108	C₂³×D₄₇	C₂²⋊C₄	1	4	yes	—
109	C₂³×D₄₇	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	—	2	2	no	—
126	C₂×D₁₈₈	—	2	2	no	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	—	2	2	no	—
131	C₂×D₁₈₈	—	2	2	no	—
132	C₂×D₁₈₈	—	2	2	no	—
133	C₂×D₁₈₈	—	2	2	no	—
134	C₂×D₁₈₈	—	2	2	no	—
135	C₂×D₁₈₈	—	2	2	no	—
136	C₂×D₁₈₈	—	2	2	no	—
137	C₂×D₁₈₈	—	2	2	no	—
138	C₂×D₁₈₈	—	2	2	no	—
139	C₂×D₁₈₈	—	2	2	no	—
140	C₂×D₁₈₈	—	2	2	no	—
141	C₂×D₁₈₈	—	2	2	no	—
142	C₂×D₁₈₈	—	2	2	no	—
143	C₂×D₁₈₈	—	2	2	no	—
144	C₂×D₁₈₈	—	2	2	no	—
145	C₂×D₁₈₈	—	2	2	no	—
146	C₂×D₁₈₈	—	2	2	no	—
147	C₂×D₁₈₈	—	2	2	no	—
148	C₂×D₁₈₈	—	2	2	no	—
149	C₂×D₁₈₈	—	2	2	no	—
150	C₂×D₁₈₈	C₂²⋊C₄	1	4	yes	—
151	C₂×D₁₈₈	C₂²⋊C₄	1	4	yes	—
152	C₂×D₁₈₈	C₂×D₄	1	4	yes	—
153	C₂×D₁₈₈	C₂×D₄	1	4	yes	—
154	C₂×C₄×D₄₇	—	2	16	no	—
155	C₂×C₄×D₄₇	—	8	8	no	—
156	M₁₆×C₄₇	—	2	2	no	—
157	M₁₆×C₄₇	—	2	2	no	—
158	M₁₆×C₄₇	—	2	2	no	—
159	M₁₆×C₄₇	—	2	2	no	—
160	M₁₆×C₄₇	—	4	1	no	—
161	M₁₆×C₄₇	—	4	1	no	—
162	M₁₆×C₄₇	—	4	1	no	—
163	M₁₆×C₄₇	—	4	1	no	—
164	C₂×C₈×C₄₇	—	2	2	no	—
165	C₂×C₈×C₄₇	—	2	2	no	—
166	C₂×C₈×C₄₇	—	4	1	no	—
167	C₂×C₈×C₄₇	—	4	1	no	—
168	C₂×C₈×C₄₇	—	4	1	no	—
169	C₂×C₈×C₄₇	—	4	1	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
174	C₄²×C₄₇	—	2	2	no	—
175	C₄²×C₄₇	—	2	2	no	—
176	C₂²⋊Dic₄₇	—	2	2	no	—
177	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
178	(C₂×D₄₇)⋊C₄	—	2	16	no	—
179	C₄⋊Dic₄₇	—	2	2	no	—
180	C₄⋊Dic₄₇	—	2	2	no	—
181	C₄×Dic₄₇	—	2	2	no	—
182	C₄×Dic₄₇	—	2	2	no	—
183	#10625329	—	2	2	no	—
184	#10625329	—	2	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	—	2	2	no	—
187	#10625329	—	4	1	no	—
188	#10625329	—	4	1	no	—
189	#10625329	—	4	1	no	—
190	#10625329	—	4	1	no	—
191	C₂×C₄₇⋊C₈	—	2	2	no	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	C₂×C₄₇⋊C₈	—	4	1	no	—
194	C₂×C₄₇⋊C₈	—	4	1	no	—
195	C₂×C₄₇⋊C₈	—	4	1	no	—
196	C₂×C₄₇⋊C₈	—	4	1	no	—
197	C₂³×C₄₇	—	4	2	no	—
198	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₄₇	#117	1	1	yes	characteristic
201	C₂³×C₄₇	#117	1	1	yes	characteristic
202	C₂³×C₄₇	#117	1	1	yes	characteristic
203	C₂³×C₄₇	#117	1	1	yes	characteristic
204	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
205	C₂²×D₄₇	—	2	4	no	—
206	C₂²×D₄₇	—	2	4	no	—
207	C₂²×D₄₇	—	2	4	no	—
208	C₂²×D₄₇	—	2	4	no	—
209	C₂²×D₄₇	—	2	4	no	—
210	C₂²×D₄₇	—	2	4	no	—
211	C₂²×D₄₇	—	4	8	no	—
212	C₂²×D₄₇	—	8	4	no	—
213	C₂²×D₄₇	—	8	4	no	—
214	C₂²×D₄₇	—	8	4	no	—
215	C₂²×D₄₇	—	8	4	no	—
216	C₂²×D₄₇	—	8	4	no	—
217	C₂²×D₄₇	—	8	4	no	—
218	C₂²×D₄₇	C₂×C₂²⋊C₄	1	8	yes	—
219	C₂×C₄×C₄₇	—	2	4	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
225	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
226	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
227	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
249	C₂×Dic₄₇	—	2	4	no	—
250	C₂×Dic₄₇	—	4	4	no	—
251	D₁₈₈	—	2	4	no	—
252	D₁₈₈	—	2	4	no	—
253	D₁₈₈	—	2	4	no	—
254	D₁₈₈	—	2	4	no	—
255	D₁₈₈	—	2	4	no	—
256	D₁₈₈	—	2	4	no	—
257	D₁₈₈	—	2	4	no	—
258	D₁₈₈	—	2	4	no	—
259	C₄×D₄₇	—	8	16	no	—
260	C₈×C₄₇	—	4	2	no	—
261	C₈×C₄₇	—	4	2	no	—
262	C₄₇⋊C₈	—	4	2	no	—
263	C₄₇⋊C₈	—	4	2	no	—
264	C₂×#1829	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	—	4	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	#381	1	1	yes	characteristic
273	C₂²×C₄₇	#381	1	1	yes	characteristic
274	C₂²×C₄₇	#381	1	1	yes	characteristic
275	C₂²×C₄₇	#381	1	1	yes	characteristic
276	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
278	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
279	C₂×D₄₇	—	2	8	no	—
280	C₂×D₄₇	—	4	8	no	—
281	C₂×D₄₇	—	4	8	no	—
282	C₂×D₄₇	—	4	8	no	—
283	C₂×D₄₇	—	8	4	no	—
284	C₂×D₄₇	—	8	4	no	—
285	C₂×D₄₇	—	8	4	no	—
286	C₂×D₄₇	—	8	4	no	—
287	C₄×C₄₇	—	4	4	no	—
288	C₄×C₄₇	#381	1	1	yes	characteristic
289	C₄×C₄₇	#381	1	1	yes	characteristic
290	C₄×C₄₇	#381	1	1	yes	characteristic
291	C₄×C₄₇	#381	1	1	yes	characteristic
292	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
293	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
294	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
295	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
296	Dic₄₇	—	4	4	no	—
297	C₂×#518	—	47	1	no	—
298	C₂²×#100	—	47	1	no	—
299	C₂²×#100	—	47	1	no	—
300	#1829	—	47	8	no	—
301	C₂×#344	—	47	1	no	—
302	C₂×#344	—	47	1	no	—
303	C₂×#344	—	47	1	no	—
304	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
305	C₂×C₄₇	—	2	1	no	—
306	C₂×C₄₇	—	2	1	no	—
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	#1829	1	2	yes	complemented
312	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
313	D₄₇	—	4	8	no	—
314	C₂³×D₄	—	47	1	no	—
315	C₂²×M₁₆	—	47	1	no	—
316	C₂²×M₁₆	—	47	1	no	—
317	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
318	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
319	#518	—	47	4	no	—
320	#518	—	47	4	no	—
321	#518	—	94	2	no	—
322	#518	—	94	2	no	—
323	C₂×C₄×D₄	—	94	2	no	—
324	C₂×C₄×D₄	—	94	2	no	—
325	C₂×#117	—	47	1	no	—
326	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	—	47	4	no	—
328	C₂×#100	—	47	4	no	—
329	C₂×#100	—	47	4	no	—
330	C₂×#100	—	94	2	no	—
331	C₂×#100	—	94	2	no	—
332	C₂×#100	—	94	2	no	—
333	C₂×#100	—	94	2	no	—
334	#344	—	47	4	no	—
335	#344	—	47	4	no	—
336	#344	—	47	4	no	—
337	#344	C₂×D₄₇	1	4	yes	complemented
338	C₄₇	C₂×#1829	1	1	yes	characteristic, complemented, Sylow
339	C₂⁵	—	47	2	no	—
340	C₂²×D₄	—	47	2	no	—
341	C₂²×D₄	—	47	2	no	—
342	C₂²×D₄	—	47	2	no	—
343	C₂²×D₄	—	47	2	no	—
344	C₂²×D₄	—	47	2	no	—
345	C₂²×D₄	—	47	2	no	—
346	C₂²×D₄	—	94	1	no	—
347	C₂²×D₄	—	94	1	no	—
348	C₂²×D₄	—	94	1	no	—
349	C₂²×D₄	—	94	1	no	—
350	C₂²×D₄	—	94	1	no	—
351	C₂²×D₄	—	94	1	no	—
352	C₂²×D₄	—	94	1	no	—
353	C₂²×D₄	—	94	1	no	—
354	C₂³×C₄	—	94	4	no	—
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	47	2	no	—
367	C₂×M₁₆	—	47	2	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂×M₁₆	—	94	1	no	—
370	C₂×M₁₆	—	94	1	no	—
371	C₂×M₁₆	—	94	1	no	—
372	C₂×M₁₆	—	94	1	no	—
373	C₂×M₁₆	—	94	1	no	—
374	C₂×M₁₆	—	94	1	no	—
375	C₂×M₁₆	—	94	1	no	—
376	C₂×M₁₆	—	94	1	no	—
377	C₂×M₁₆	—	94	1	no	—
378	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
379	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	94	1	no	—
383	C₂²×C₈	—	94	1	no	—
384	C₄×D₄	—	94	8	no	—
385	C₄×D₄	—	94	8	no	—
386	C₄×D₄	—	94	8	no	—
387	C₄×D₄	—	94	8	no	—
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	47	2	no	—
391	#117	—	47	2	no	—
392	#117	—	94	1	no	—
393	#117	—	94	1	no	—
394	#117	C₄×D₄₇	1	2	yes	—
395	#117	C₂²×D₄₇	1	2	yes	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	94	1	no	—
398	C₂×C₂²⋊C₄	—	47	2	no	—
399	C₂×C₂²⋊C₄	—	47	16	no	—
400	C₂×C₂²⋊C₄	—	94	8	no	—
401	C₂×C₂²⋊C₄	—	94	4	no	—
402	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	94	1	no	—
405	#100	—	94	8	no	—
406	#100	—	94	8	no	—
407	C₂⁴	—	47	4	no	—
408	C₂⁴	—	47	4	no	—
409	C₂⁴	—	47	4	no	—
410	C₂⁴	—	94	2	no	—
411	C₂⁴	—	94	2	no	—
412	C₂⁴	—	94	2	no	—
413	C₂⁴	—	94	2	no	—
414	C₂⁴	—	376	4	no	—
415	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
416	C₂×D₄	—	47	4	no	—
417	C₂×D₄	—	47	4	no	—
418	C₂×D₄	—	47	4	no	—
419	C₂×D₄	—	47	4	no	—
420	C₂×D₄	—	94	2	no	—
421	C₂×D₄	—	94	2	no	—
422	C₂×D₄	—	94	2	no	—
423	C₂×D₄	—	94	2	no	—
424	C₂×D₄	—	94	2	no	—
425	C₂×D₄	—	94	2	no	—
426	C₂×D₄	—	94	2	no	—
427	C₂×D₄	—	94	2	no	—
428	C₂×D₄	—	94	2	no	—
429	C₂×D₄	—	94	2	no	—
430	C₂×D₄	—	94	2	no	—
431	C₂×D₄	—	94	2	no	—
432	C₂×D₄	—	94	2	no	—
433	C₂×D₄	—	94	2	no	—
434	C₂×D₄	—	94	2	no	—
435	C₂×D₄	—	94	2	no	—
436	C₂×D₄	—	94	2	no	—
437	C₂×D₄	—	94	2	no	—
438	C₂×D₄	—	94	2	no	—
439	C₂×D₄	—	94	2	no	—
440	C₂×D₄	—	94	2	no	—
441	C₂×D₄	—	94	2	no	—
442	C₂×D₄	—	94	2	no	—
443	C₂×D₄	—	94	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	94	16	no	—
446	C₂²×C₄	—	94	2	no	—
447	C₂²×C₄	—	376	8	no	—
448	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
449	C₂²×C₄	#10625350	1	1	yes	characteristic
450	C₂²×C₄	#10625350	1	1	yes	characteristic
451	C₂²×C₄	#10625350	1	1	yes	characteristic
452	C₂²×C₄	#10625350	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
457	C₂²×C₄	#10625352	1	1	yes	characteristic
458	C₂²×C₄	#10625352	1	1	yes	characteristic
459	C₂²×C₄	#10625354	1	1	yes	characteristic
460	C₂²×C₄	#10625354	1	1	yes	characteristic
461	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	94	2	no	—
471	M₁₆	—	94	2	no	—
472	M₁₆	—	94	2	no	—
473	M₁₆	—	94	2	no	—
474	M₁₆	—	188	1	no	—
475	M₁₆	—	188	1	no	—
476	M₁₆	—	188	1	no	—
477	M₁₆	—	188	1	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	94	2	no	—
485	C₂×C₈	—	94	2	no	—
486	C₂×C₈	—	188	1	no	—
487	C₂×C₈	—	188	1	no	—
488	C₂×C₈	—	188	1	no	—
489	C₂×C₈	—	188	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	94	2	no	—
493	C₄⋊C₄	—	94	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	47	4	no	—
496	C₂²⋊C₄	—	94	16	no	—
497	C₂²⋊C₄	—	94	2	no	—
498	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	94	2	no	—
502	C₄²	—	94	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	47	8	no	—
505	C₂³	—	94	4	no	—
506	C₂³	—	94	4	no	—
507	C₂³	—	94	4	no	—
508	C₂³	—	94	4	no	—
509	C₂³	—	94	4	no	—
510	C₂³	—	94	4	no	—
511	C₂³	—	376	4	no	—
512	C₂³	—	376	4	no	—
513	C₂³	—	376	4	no	—
514	C₂³	—	376	4	no	—
515	C₂³	—	376	4	no	—
516	C₂³	—	376	4	no	—
517	C₂³	—	188	8	no	—
518	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
519	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
520	C₂³	#13093981	1	1	yes	characteristic
521	C₂³	#13093981	1	1	yes	characteristic
522	C₂³	#13093982	1	1	yes	characteristic
523	C₂³	#13093982	1	1	yes	characteristic
524	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
525	D₄	—	94	4	no	—
526	D₄	—	94	4	no	—
527	D₄	—	94	4	no	—
528	D₄	—	94	4	no	—
529	D₄	—	94	4	no	—
530	D₄	—	94	4	no	—
531	D₄	—	94	4	no	—
532	D₄	—	94	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	94	4	no	—
536	C₂×C₄	—	376	16	no	—
537	C₂×C₄	—	188	4	no	—
538	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
540	C₂×C₄	#13093981	1	1	yes	characteristic
541	C₂×C₄	#13093981	1	1	yes	characteristic
542	C₂×C₄	#13093982	1	1	yes	characteristic
543	C₂×C₄	#13093982	1	1	yes	characteristic
544	C₂×C₄	#13094006	1	1	yes	characteristic
545	C₂×C₄	#13094006	1	1	yes	characteristic
546	C₂×C₄	#13094006	1	1	yes	characteristic
547	C₂×C₄	#13094006	1	1	yes	characteristic
548	C₂×C₄	#13094006	1	1	yes	characteristic
549	C₂×C₄	#13094006	1	1	yes	characteristic
550	C₂×C₄	#13094006	1	1	yes	characteristic
551	C₂×C₄	#13094006	1	1	yes	characteristic
552	C₂×C₄	#13094009	1	1	yes	characteristic
553	C₂×C₄	#13094009	1	1	yes	characteristic
554	C₂×C₄	#13094009	1	1	yes	characteristic
555	C₂×C₄	#13094009	1	1	yes	characteristic
556	C₂×C₄	#13094009	1	1	yes	characteristic
557	C₂×C₄	#13094009	1	1	yes	characteristic
558	C₂×C₄	#13094009	1	1	yes	characteristic
559	C₂×C₄	#13094009	1	1	yes	characteristic
560	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
561	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
562	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
563	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
564	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
565	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
566	C₈	—	4	2	no	—
567	C₈	—	4	2	no	—
568	C₈	—	188	2	no	—
569	C₈	—	188	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	94	8	no	—
578	C₂²	—	376	4	no	—
579	C₂²	—	376	4	no	—
580	C₂²	—	376	4	no	—
581	C₂²	—	376	4	no	—
582	C₂²	—	188	8	no	—
583	C₂²	—	188	8	no	—
584	C₂²	—	188	8	no	—
585	C₂²	#15688985	1	1	yes	characteristic
586	C₂²	#15688985	1	1	yes	characteristic
587	C₂²	#15688985	1	1	yes	characteristic
588	C₂²	#15688985	1	1	yes	characteristic
589	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
590	C₂²	C₂×#13093981	1	1	yes	characteristic
591	C₂²	C₂×#13093982	1	1	yes	characteristic
592	C₄	—	4	4	no	—
593	C₄	—	188	4	no	—
594	C₄	#15688985	1	1	yes	characteristic
595	C₄	#15688985	1	1	yes	characteristic
596	C₄	#15688985	1	1	yes	characteristic
597	C₄	#15688985	1	1	yes	characteristic
598	C₄	C₂×#13094006	1	1	yes	characteristic
599	C₄	C₂×#13094006	1	1	yes	characteristic
600	C₄	C₂×#13094009	1	1	yes	characteristic
601	C₄	C₂×#13094009	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	188	8	no	—
609	C₂	#20243498	1	2	yes	direct product factor
610	C₂	C₂×#15688985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15688985
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂²×C₄₇	#381
prime radical	C₂³×D₁₈₈	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	C₂×#1829
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. #20243498	C₂	direct (N × H)
5. C₂×#15688895	C₂	semidirect
6. C₂×#15688894	C₂	semidirect
7. C₂×#15688893	C₂	semidirect
8. C₂×C₄₇×#344	C₂	semidirect
26. #15688895	C₂²	semidirect
27. #15688894	C₂²	semidirect
28. #15688893	C₂²	semidirect
32. C₄₇×#344	C₂²	semidirect
304. C₂×#344	D₄₇	semidirect
311. C₂×C₄₇	#1829	semidirect
337. #344	C₂×D₄₇	semidirect
338. C₄₇	C₂×#1829	semidirect
609. C₂	#20243498	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×#15689597	2
C₂²×#13093940	2
#20243498	2
C₂×#15688895	2
C₂×#15688894	2
C₂×#15688893	2
C₂×C₄₇×#344	2
C₂×#1829	47

Subgroups — C2×#20243498 #26216140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243498 #26216140