Subgroups — C₂×#20244286 #26220252

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094046	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689139	C₂	1	2	yes	maximal, complemented
4	C₂×#15689096	C₂	1	2	yes	maximal, complemented
5	#20244286	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10625350	C₂²	1	2	yes	—
8	C₂×#13094046	—	2	1	no	—
9	C₂×#13094046	—	2	1	no	—
10	C₂×#13094046	—	2	2	no	—
11	C₂×#13094046	—	2	1	no	—
12	C₂×#13094046	—	2	1	no	—
13	C₂×#13094046	—	2	2	no	—
14	C₂×#13094046	C₄	1	4	yes	complemented
15	C₂×#13094046	C₂²	1	4	yes	—
16	C₂²×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
17	C₂²×#10625325	C₄	1	2	yes	complemented
18	C₂²×D₃₇₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#13093983	C₂²	1	2	yes	—
20	#15689161	—	2	2	no	—
21	#15689161	C₂²	1	4	yes	complemented
22	C₂×#13093958	—	2	1	no	—
23	C₂×#13093956	—	2	1	no	—
24	#15689139	—	2	4	no	—
25	#15689139	C₂²	1	8	yes	complemented
26	C₂×#13093950	—	2	4	no	—
27	#15689096	—	2	4	no	—
28	#15689096	C₂²	1	8	yes	complemented
29	C₂×#13093938	—	2	4	no	—
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#405	—	2	2	no	—
34	C₄₇×#405	C₂²	1	4	yes	complemented
35	C₂×#97×C₄₇	—	2	1	no	—
36	C₂×C₄×C₈×C₄₇	—	2	1	no	—
37	C₂×#10625350	—	2	2	no	—
38	C₂×#10625350	—	2	2	no	—
39	C₂×#10625350	—	2	2	no	—
40	C₂×#10625350	—	2	2	no	—
41	C₂×#10625350	—	2	2	no	—
42	C₂×#10625350	—	2	2	no	—
43	C₂×#10625350	—	2	2	no	—
44	C₂×#10625350	—	2	2	no	—
45	C₂×#10625350	—	2	2	no	—
46	C₂×#10625350	—	2	2	no	—
47	C₂×#10625350	C₂×C₄	1	4	yes	—
48	C₂×#10625350	C₂³	1	4	yes	—
49	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
50	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
51	C₂²×C₂²⋊D₄₇	—	2	2	no	—
52	C₂²×C₄×D₄₇	—	2	2	no	—
53	#13094046	—	2	4	no	—
54	#13094046	—	2	4	no	—
55	#13094046	—	2	4	no	—
56	#13094046	—	2	4	no	—
57	#13094046	—	2	4	no	—
58	#13094046	—	2	4	no	—
59	#13094046	—	2	4	no	—
60	#13094046	—	2	4	no	—
61	C₂×Dic₁₈₈	—	2	1	no	—
62	C₂×Dic₁₈₈	—	2	1	no	—
63	C₂×Dic₁₈₈	—	2	2	no	—
64	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	complemented
65	C₂×#10625325	—	2	2	no	—
66	C₂×#10625325	—	2	2	no	—
67	C₂×#10625325	—	2	4	no	—
68	C₂×#10625325	C₂×C₄	1	8	yes	complemented
69	C₂×D₃₇₆	—	2	1	no	—
70	C₂×D₃₇₆	—	2	1	no	—
71	C₂×D₃₇₆	—	2	2	no	—
72	C₂×D₃₇₆	C₂×C₄	1	4	yes	complemented
73	#13093983	—	2	2	no	—
74	#13093983	—	2	2	no	—
75	#13093983	—	2	2	no	—
76	#13093983	C₂³	1	4	yes	—
77	C₂×C₄⋊Dic₄₇	—	2	2	no	—
78	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
79	C₂×C₄×Dic₄₇	—	2	2	no	—
80	#13093958	—	2	4	no	—
81	#13093956	—	2	4	no	—
82	#13093950	—	2	16	no	—
83	#13093938	—	2	16	no	—
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
90	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	D₄	1	2	yes	—
98	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	D₄	1	2	yes	—
101	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	D₄	1	2	yes	—
105	#117×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
108	C₂×C₄²×C₄₇	—	2	1	no	—
109	#97×C₄₇	—	2	4	no	—
110	C₄×C₈×C₄₇	—	2	4	no	—
111	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂³×D₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂×C₂²⋊D₄₇	—	2	4	no	—
129	C₂×C₂²⋊D₄₇	—	2	4	no	—
130	C₂×C₂²⋊D₄₇	—	4	2	no	—
131	C₂×C₂²⋊D₄₇	—	4	2	no	—
132	C₂×C₂²⋊D₄₇	—	4	2	no	—
133	C₂×C₂²⋊D₄₇	—	4	2	no	—
134	C₂²×Dic₄₇	—	2	2	no	—
135	C₂²×Dic₄₇	—	4	2	no	—
136	#10625350	—	2	4	no	—
137	#10625350	—	2	4	no	—
138	#10625350	—	2	4	no	—
139	#10625350	—	2	4	no	—
140	#10625350	—	2	4	no	—
141	#10625350	—	2	4	no	—
142	#10625350	—	2	4	no	—
143	#10625350	—	2	4	no	—
144	#10625350	—	4	2	no	—
145	#10625350	—	4	2	no	—
146	#10625350	—	4	2	no	—
147	#10625350	—	4	2	no	—
148	#10625350	—	4	2	no	—
149	#10625350	—	4	2	no	—
150	#10625350	—	4	2	no	—
151	#10625350	—	4	2	no	—
152	C₂×D₁₈₈	—	2	2	no	—
153	C₂×D₁₈₈	—	2	2	no	—
154	C₂×D₁₈₈	—	2	2	no	—
155	C₂×D₁₈₈	—	2	2	no	—
156	C₂×D₁₈₈	—	2	2	no	—
157	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
158	C₂×C₄×D₄₇	—	2	4	no	—
159	C₂×C₄×D₄₇	—	2	4	no	—
160	C₂×C₄×D₄₇	—	4	2	no	—
161	C₂×C₄×D₄₇	—	4	2	no	—
162	C₂×C₄×D₄₇	—	4	2	no	—
163	C₂×C₄×D₄₇	—	4	2	no	—
164	C₂×Dic₉₄	—	2	2	no	—
165	C₂×Dic₉₄	—	2	2	no	—
166	C₂×Dic₉₄	—	2	2	no	—
167	C₂×Dic₉₄	—	2	2	no	—
168	C₂×Dic₉₄	—	2	2	no	—
169	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
170	M₁₆×C₄₇	—	2	2	no	—
171	M₁₆×C₄₇	—	2	2	no	—
172	M₁₆×C₄₇	—	2	2	no	—
173	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
174	C₂×C₈×C₄₇	—	2	2	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
180	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
183	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
184	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
185	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
186	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
187	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
189	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₄₇	—	2	2	no	—
194	C₄⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	2	no	—
196	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
197	C₄²×C₄₇	—	2	2	no	—
198	C₄²×C₄₇	—	2	2	no	—
199	C₂²⋊Dic₄₇	—	2	4	no	—
200	C₂²⋊Dic₄₇	—	4	2	no	—
201	C₄⋊Dic₄₇	—	2	4	no	—
202	C₄⋊Dic₄₇	—	4	2	no	—
203	C₄×Dic₄₇	—	2	4	no	—
204	C₄×Dic₄₇	—	4	2	no	—
205	Dic₁₈₈	—	2	4	no	—
206	Dic₁₈₈	—	2	4	no	—
207	D₃₇₆	—	2	4	no	—
208	D₃₇₆	—	2	4	no	—
209	#10625325	—	2	8	no	—
210	#10625325	—	2	8	no	—
211	C₂³×C₄₇	—	4	2	no	—
212	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₇	#121	1	1	yes	characteristic
215	C₂³×C₄₇	#121	1	1	yes	characteristic
216	C₂³×C₄₇	#127	1	1	yes	characteristic
217	C₂³×C₄₇	#127	1	1	yes	characteristic
218	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
219	C₂²×D₄₇	—	2	4	no	—
220	C₂²×D₄₇	—	4	2	no	—
221	C₂²×D₄₇	—	4	2	no	—
222	C₂²×D₄₇	—	8	4	no	—
223	C₂×C₄×C₄₇	—	2	4	no	—
224	C₂×C₄×C₄₇	—	4	4	no	—
225	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂²⋊D₄₇	—	4	4	no	—
254	C₂²⋊D₄₇	—	4	4	no	—
255	C₂²⋊D₄₇	—	4	4	no	—
256	C₂²⋊D₄₇	—	4	4	no	—
257	C₂×Dic₄₇	—	2	4	no	—
258	C₂×Dic₄₇	—	4	2	no	—
259	C₂×Dic₄₇	—	4	2	no	—
260	C₂×Dic₄₇	—	4	4	no	—
261	C₂×Dic₄₇	—	8	4	no	—
262	D₁₈₈	—	2	4	no	—
263	D₁₈₈	—	2	4	no	—
264	D₁₈₈	—	4	2	no	—
265	D₁₈₈	—	4	2	no	—
266	C₄×D₄₇	—	4	4	no	—
267	C₄×D₄₇	—	4	4	no	—
268	C₄×D₄₇	—	4	4	no	—
269	C₄×D₄₇	—	4	4	no	—
270	Dic₉₄	—	2	4	no	—
271	Dic₉₄	—	2	4	no	—
272	Dic₉₄	—	4	2	no	—
273	Dic₉₄	—	4	2	no	—
274	C₈×C₄₇	—	2	4	no	—
275	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
276	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
277	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
278	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂×#1976	—	47	1	no	maximal, Sylow
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	#390	1	1	yes	characteristic
288	C₂²×C₄₇	#390	1	1	yes	characteristic
289	C₂²×C₄₇	#390	1	1	yes	characteristic
290	C₂²×C₄₇	#390	1	1	yes	characteristic
291	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
293	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
294	C₂×D₄₇	—	4	4	no	—
295	C₂×D₄₇	—	8	4	no	—
296	C₂×D₄₇	—	8	4	no	—
297	C₂×D₄₇	—	8	4	no	—
298	C₄×C₄₇	—	4	4	no	—
299	C₄×C₄₇	#390	1	1	yes	characteristic
300	C₄×C₄₇	#390	1	1	yes	characteristic
301	C₄×C₄₇	#390	1	1	yes	characteristic
302	C₄×C₄₇	#390	1	1	yes	characteristic
303	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
305	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
306	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
307	Dic₄₇	—	4	4	no	—
308	Dic₄₇	—	8	4	no	—
309	C₂²×#135	—	47	1	no	—
310	C₂×#427	—	47	1	no	—
311	C₂×#421	—	47	2	no	—
312	C₂×#410	—	47	2	no	—
313	C₂×#405	D₄₇	1	1	yes	characteristic, complemented
314	#1976	—	47	8	no	—
315	C₂×C₄₇	—	2	1	no	—
316	C₂×C₄₇	—	2	1	no	—
317	C₂×C₄₇	—	2	1	no	—
318	C₂×C₄₇	—	2	1	no	—
319	C₂×C₄₇	—	2	1	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	#1976	1	2	yes	complemented
322	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
323	D₄₇	—	8	4	no	—
324	C₂²×#41	—	47	2	no	—
325	C₂×#135	—	47	4	no	—
326	C₂×#135	—	47	4	no	—
327	C₂×#135	—	94	1	no	—
328	C₂×#135	—	94	1	no	—
329	C₂×#135	—	94	2	no	—
330	C₂×#135	—	94	1	no	—
331	C₂×#135	—	94	1	no	—
332	C₂×#135	—	94	2	no	—
333	C₂²×Q₁₆	—	47	1	no	—
334	C₂²×SD₁₆	—	47	2	no	—
335	C₂²×D₈	—	47	1	no	—
336	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
337	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
338	C₂×#117	—	47	2	no	—
339	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
340	#427	—	47	4	no	—
341	#427	—	94	2	no	—
342	C₂×#107	—	94	1	no	—
343	C₂×#106	—	94	1	no	—
344	#421	—	47	8	no	—
345	#421	—	94	4	no	—
346	C₂×#104	—	94	4	no	—
347	#410	—	47	8	no	—
348	#410	—	94	4	no	—
349	C₂×#99	—	94	4	no	—
350	#405	—	2	2	no	—
351	#405	C₂×D₄₇	1	4	yes	complemented
352	C₂×#97	—	2	1	no	—
353	C₂×C₄×C₈	—	2	1	no	—
354	C₄₇	C₂×#1976	1	1	yes	characteristic, complemented, Sylow
355	C₂×#41	—	47	4	no	—
356	C₂×#41	—	47	4	no	—
357	C₂×#41	—	94	2	no	—
358	C₂×#41	—	94	2	no	—
359	C₂×#41	—	94	2	no	—
360	C₂×#41	—	94	2	no	—
361	C₂×#41	—	94	2	no	—
362	C₂×#41	—	94	2	no	—
363	C₂×#41	—	94	2	no	—
364	C₂×#41	—	94	2	no	—
365	C₂×#41	—	94	2	no	—
366	C₂×#41	—	94	2	no	—
367	C₂²×Q₈	—	47	2	no	—
368	C₂²×D₄	—	47	2	no	—
369	C₂²×D₄	—	94	2	no	—
370	C₂³×C₄	—	94	2	no	—
371	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
372	#135	—	94	4	no	—
373	#135	—	94	4	no	—
374	#135	—	94	4	no	—
375	#135	—	94	4	no	—
376	#135	—	94	4	no	—
377	#135	—	94	4	no	—
378	#135	—	94	4	no	—
379	#135	—	94	4	no	—
380	C₂×Q₁₆	—	47	4	no	—
381	C₂×Q₁₆	—	94	1	no	—
382	C₂×Q₁₆	—	94	1	no	—
383	C₂×Q₁₆	—	94	2	no	—
384	C₂×SD₁₆	—	47	8	no	—
385	C₂×SD₁₆	—	94	2	no	—
386	C₂×SD₁₆	—	94	2	no	—
387	C₂×SD₁₆	—	94	4	no	—
388	C₂×D₈	—	47	4	no	—
389	C₂×D₈	—	94	1	no	—
390	C₂×D₈	—	94	1	no	—
391	C₂×D₈	—	94	2	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	D₁₈₈	1	2	yes	—
396	C₂×M₁₆	D₁₈₈	1	2	yes	—
397	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
400	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
401	C₂²×C₈	C₄×D₄₇	1	2	yes	—
402	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
403	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
404	C₂²×C₈	D₁₈₈	1	2	yes	—
405	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
407	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
408	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	47	4	no	—
412	#117	—	94	2	no	—
413	#117	—	94	2	no	—
414	#117	—	94	2	no	—
415	#117	D₁₈₈	1	2	yes	—
416	#117	C₂²×D₄₇	1	2	yes	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	94	2	no	—
419	C₂×C₂²⋊C₄	—	94	2	no	—
420	C₂×C₂²⋊C₄	D₁₈₈	1	2	yes	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	94	2	no	—
423	#107	—	94	4	no	—
424	#106	—	94	4	no	—
425	#104	—	94	16	no	—
426	#99	—	94	16	no	—
427	#97	—	2	4	no	—
428	C₄×C₈	—	2	4	no	—
429	C₂⁴	—	94	2	no	—
430	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
431	#41	—	94	4	no	—
432	#41	—	94	4	no	—
433	#41	—	94	4	no	—
434	#41	—	94	4	no	—
435	#41	—	94	4	no	—
436	#41	—	94	4	no	—
437	#41	—	94	4	no	—
438	#41	—	94	4	no	—
439	#41	—	188	2	no	—
440	#41	—	188	2	no	—
441	#41	—	188	2	no	—
442	#41	—	188	2	no	—
443	#41	—	188	2	no	—
444	#41	—	188	2	no	—
445	#41	—	188	2	no	—
446	#41	—	188	2	no	—
447	C₂×Q₈	—	47	4	no	—
448	C₂×Q₈	—	94	2	no	—
449	C₂×Q₈	—	94	2	no	—
450	C₂×Q₈	—	94	2	no	—
451	C₂×Q₈	—	94	2	no	—
452	C₂×Q₈	—	94	2	no	—
453	C₂×D₄	—	47	4	no	—
454	C₂×D₄	—	94	4	no	—
455	C₂×D₄	—	94	4	no	—
456	C₂×D₄	—	94	2	no	—
457	C₂×D₄	—	94	2	no	—
458	C₂×D₄	—	94	2	no	—
459	C₂×D₄	—	94	2	no	—
460	C₂×D₄	—	94	2	no	—
461	C₂×D₄	—	188	2	no	—
462	C₂×D₄	—	188	2	no	—
463	C₂×D₄	—	188	2	no	—
464	C₂×D₄	—	188	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	94	2	no	—
467	C₂²×C₄	—	94	4	no	—
468	C₂²×C₄	—	94	4	no	—
469	C₂²×C₄	—	188	2	no	—
470	C₂²×C₄	—	188	2	no	—
471	C₂²×C₄	—	188	2	no	—
472	C₂²×C₄	—	188	2	no	—
473	C₂²×C₄	—	188	2	no	—
474	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
481	C₂²×C₄	#10625350	1	1	yes	characteristic
482	C₂²×C₄	#10625350	1	1	yes	characteristic
483	C₂²×C₄	#10625350	1	1	yes	characteristic
484	C₂²×C₄	#10625350	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
487	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
488	Q₁₆	—	94	4	no	—
489	Q₁₆	—	94	4	no	—
490	SD₁₆	—	94	8	no	—
491	SD₁₆	—	94	8	no	—
492	D₈	—	94	4	no	—
493	D₈	—	94	4	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	C₂×D₁₈₈	1	4	yes	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
502	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
503	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
504	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
505	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
506	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
507	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
508	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
509	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
510	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
511	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
512	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
513	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
514	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
515	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
516	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	94	4	no	—
520	C₄⋊C₄	—	188	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	94	4	no	—
523	C₂²⋊C₄	—	188	2	no	—
524	C₂²⋊C₄	C₂×D₁₈₈	1	4	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	94	4	no	—
528	C₄²	—	188	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	94	4	no	—
531	C₂³	—	376	4	no	—
532	C₂³	—	188	2	no	—
533	C₂³	—	188	2	no	—
534	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
535	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
536	C₂³	#13093998	1	1	yes	characteristic
537	C₂³	#13093998	1	1	yes	characteristic
538	C₂³	#13094021	1	1	yes	characteristic
539	C₂³	#13094021	1	1	yes	characteristic
540	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
541	Q₈	—	94	4	no	—
542	Q₈	—	94	4	no	—
543	Q₈	—	188	2	no	—
544	Q₈	—	188	2	no	—
545	D₄	—	94	4	no	—
546	D₄	—	94	4	no	—
547	D₄	—	188	4	no	—
548	D₄	—	188	4	no	—
549	D₄	—	188	4	no	—
550	D₄	—	188	4	no	—
551	D₄	—	188	2	no	—
552	D₄	—	188	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	94	4	no	—
556	C₂×C₄	—	376	4	no	—
557	C₂×C₄	—	188	4	no	—
558	C₂×C₄	—	188	2	no	—
559	C₂×C₄	—	188	2	no	—
560	C₂×C₄	—	188	4	no	—
561	C₂×C₄	—	188	4	no	—
562	C₂×C₄	—	188	4	no	—
563	C₂×C₄	—	188	4	no	—
564	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
569	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
570	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
571	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
572	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
573	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
574	C₂×C₄	#13093998	1	1	yes	characteristic
575	C₂×C₄	#13093998	1	1	yes	characteristic
576	C₂×C₄	#13093998	1	1	yes	characteristic
577	C₂×C₄	#13093998	1	1	yes	characteristic
578	C₂×C₄	#13093998	1	1	yes	characteristic
579	C₂×C₄	#13093998	1	1	yes	characteristic
580	C₂×C₄	#13094012	1	1	yes	characteristic
581	C₂×C₄	#13094012	1	1	yes	characteristic
582	C₂×C₄	#13094012	1	1	yes	characteristic
583	C₂×C₄	#13094012	1	1	yes	characteristic
584	C₂×C₄	#13094021	1	1	yes	characteristic
585	C₂×C₄	#13094021	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
590	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
591	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
594	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
595	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
596	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	376	4	no	—
605	C₂²	—	376	4	no	—
606	C₂²	—	376	4	no	—
607	C₂²	—	188	4	no	—
608	C₂²	#15689025	1	1	yes	characteristic
609	C₂²	#15689025	1	1	yes	characteristic
610	C₂²	#15689025	1	1	yes	characteristic
611	C₂²	#15689025	1	1	yes	characteristic
612	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
613	C₂²	C₂×#13093998	1	1	yes	characteristic
614	C₂²	C₂×#13094021	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	376	4	no	—
617	C₄	—	188	4	no	—
618	C₄	#15689025	1	1	yes	characteristic
619	C₄	#15689025	1	1	yes	characteristic
620	C₄	#15689025	1	1	yes	characteristic
621	C₄	#15689025	1	1	yes	characteristic
622	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
623	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
624	C₄	C₂×#13093998	1	1	yes	characteristic
625	C₄	C₂×#13094012	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	376	4	no	—
633	C₂	#20244286	1	2	yes	direct product factor
634	C₂	C₂×#15689025	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093998
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂²×C₄₇	#390
prime radical	C₂²×#13094046	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	C₂×#1976
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#15689161	C₂	semidirect
3. C₂×#15689139	C₂	semidirect
4. C₂×#15689096	C₂	semidirect
5. #20244286	C₂	direct (N × H)
6. C₂×C₄₇×#405	C₂	semidirect
14. C₂×#13094046	C₄	semidirect
16. C₂²×Dic₁₈₈	C₄	semidirect
17. C₂²×#10625325	C₄	semidirect
18. C₂²×D₃₇₆	C₄	semidirect
21. #15689161	C₂²	semidirect
25. #15689139	C₂²	semidirect
28. #15689096	C₂²	semidirect
34. C₄₇×#405	C₂²	semidirect
64. C₂×Dic₁₈₈	C₂×C₄	semidirect
68. C₂×#10625325	C₂×C₄	semidirect
72. C₂×D₃₇₆	C₂×C₄	semidirect
313. C₂×#405	D₄₇	semidirect
321. C₂×C₄₇	#1976	semidirect
351. #405	C₂×D₄₇	semidirect
354. C₄₇	C₂×#1976	semidirect
633. C₂	#20244286	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13094046	2
C₂×#15689161	2
C₂×#15689139	2
C₂×#15689096	2
#20244286	2
C₂×C₄₇×#405	2
C₂×#1976	47

Subgroups — C2×#20244286 #26220252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244286 #26220252