Subgroups — C₂×#20243491 #26216121

Order 12032.

1354 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625350	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
4	#20243491	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₄×#10625350	—	2	2	no	—
12	C₄×#10625350	—	2	2	no	—
13	C₄×#10625350	C₄	1	4	yes	complemented
14	C₄×#10625350	C₂²	1	4	yes	—
15	C₂×C₄×Dic₉₄	—	2	1	no	—
16	C₂×C₄×D₁₈₈	—	2	1	no	—
17	C₂×C₄×C₂²⋊D₄₇	—	2	2	no	—
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	C₂×#13093981	C₄	1	2	yes	complemented
21	C₂×C₄²×D₄₇	C₄	1	2	yes	complemented
22	#15689105	—	2	2	no	—
23	#15689105	C₂²	1	4	yes	—
24	C₂×#13093942	—	2	1	no	—
25	C₂×#13093940	—	2	1	no	—
26	#15689096	—	2	2	no	—
27	#15689096	C₂²	1	4	yes	—
28	C₂×#13093938	—	2	2	no	—
29	#15688883	C₂²	1	4	yes	complemented
30	#15688880	C₂²	1	4	yes	complemented
31	#15688879	C₂²	1	4	yes	complemented
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#339	C₂²	1	4	yes	complemented
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	C₂×C₄	1	2	yes	—
45	C₂×#10625350	D₄	1	2	yes	—
46	C₂×#10625350	D₄	1	2	yes	—
47	C₂×#10625350	C₂³	1	2	yes	—
48	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
49	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
50	C₂²×C₂²⋊D₄₇	D₄	1	2	yes	—
51	C₂²×C₄×D₄₇	—	2	2	no	—
52	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
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	C₂³	1	2	yes	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₄×Dic₉₄	—	2	4	no	—
61	C₄×Dic₉₄	—	2	4	no	—
62	C₄×D₁₈₈	—	2	4	no	—
63	C₄×D₁₈₈	—	2	4	no	—
64	C₄×C₂²⋊D₄₇	—	2	8	no	—
65	C₄×C₂²⋊D₄₇	—	2	8	no	—
66	#13093983	—	2	1	no	—
67	#13093983	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093983	—	2	1	no	—
70	#13093983	—	2	1	no	—
71	#13093983	C₂×C₄	1	2	yes	—
72	#13093983	C₂³	1	2	yes	—
73	#13093983	C₂³	1	2	yes	—
74	#13093981	—	2	4	no	—
75	#13093981	C₂×C₄	1	8	yes	complemented
76	C₂×C₄⋊Dic₄₇	—	2	1	no	—
77	C₂×C₄⋊Dic₄₇	—	2	1	no	—
78	C₂×Dic₄₇⋊C₄	—	2	2	no	—
79	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
80	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
81	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
82	C₂×C₄×Dic₄₇	—	2	2	no	—
83	C₂×C₄×Dic₄₇	—	2	1	no	—
84	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
85	C₄²×D₄₇	—	2	4	no	—
86	C₄²×D₄₇	C₂×C₄	1	8	yes	complemented
87	#13093942	—	2	4	no	—
88	#13093940	—	2	4	no	—
89	#13093938	—	2	8	no	—
90	C₂³×C₄×C₄₇	—	2	1	no	—
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₄₇	—	2	1	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	1	no	—
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
98	C₂²×C₈×C₄₇	—	2	1	no	—
99	#117×C₄₇	—	2	1	no	—
100	#117×C₄₇	—	2	1	no	—
101	#117×C₄₇	—	2	1	no	—
102	#117×C₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	—	2	1	no	—
106	C₂×C₄²×C₄₇	—	2	1	no	—
107	C₂×C₄²×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	—	2	1	no	—
109	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
112	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
113	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂³×D₄₇	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	4	4	no	—
120	C₂²×C₄×C₄₇	—	4	1	no	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₇	—	2	2	no	—
136	C₂×C₂²⋊D₄₇	—	2	2	no	—
137	C₂×C₂²⋊D₄₇	—	2	2	no	—
138	C₂×C₂²⋊D₄₇	—	2	2	no	—
139	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
140	C₂×C₂²⋊D₄₇	C₂×D₄	1	4	yes	—
141	C₂²×Dic₄₇	—	2	2	no	—
142	C₂²×Dic₄₇	—	4	1	no	—
143	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	2	2	no	—
148	#10625350	—	2	2	no	—
149	#10625350	—	2	2	no	—
150	#10625350	—	2	2	no	—
151	#10625350	—	2	2	no	—
152	#10625350	—	2	2	no	—
153	#10625350	—	2	2	no	—
154	#10625350	—	2	2	no	—
155	#10625350	—	2	2	no	—
156	#10625350	—	2	2	no	—
157	#10625350	—	2	2	no	—
158	#10625350	—	2	2	no	—
159	#10625350	—	2	2	no	—
160	C₂×D₁₈₈	—	2	1	no	—
161	C₂×D₁₈₈	—	2	1	no	—
162	C₂×D₁₈₈	—	2	1	no	—
163	C₂×D₁₈₈	—	2	1	no	—
164	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
165	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
166	C₂×C₄×D₄₇	—	2	2	no	—
167	C₂×C₄×D₄₇	—	2	2	no	—
168	C₂×C₄×D₄₇	—	2	2	no	—
169	C₂×C₄×D₄₇	—	2	2	no	—
170	C₂×C₄×D₄₇	—	2	8	no	—
171	C₂×C₄×D₄₇	—	4	8	no	—
172	C₂×C₄×D₄₇	C₂²⋊C₄	1	4	yes	—
173	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
174	C₂×Dic₉₄	—	2	1	no	—
175	C₂×Dic₉₄	—	2	1	no	—
176	C₂×Dic₉₄	—	2	1	no	—
177	C₂×Dic₉₄	—	2	1	no	—
178	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
179	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
180	M₁₆×C₄₇	—	2	2	no	—
181	M₁₆×C₄₇	—	2	2	no	—
182	M₁₆×C₄₇	—	4	1	no	—
183	M₁₆×C₄₇	—	4	1	no	—
184	C₂×C₈×C₄₇	—	2	2	no	—
185	C₂×C₈×C₄₇	—	4	1	no	—
186	C₂×C₈×C₄₇	—	4	1	no	—
187	C₄⋊C₄×C₄₇	—	2	2	no	—
188	C₄⋊C₄×C₄₇	—	4	1	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	4	1	no	—
191	C₄²×C₄₇	—	2	1	no	—
192	C₄²×C₄₇	—	2	1	no	—
193	C₄²×C₄₇	—	2	2	no	—
194	C₄²×C₄₇	—	2	2	no	—
195	C₄²×C₄₇	—	2	2	no	—
196	C₄²×C₄₇	—	4	1	no	—
197	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
198	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
199	C₂²⋊Dic₄₇	—	2	2	no	—
200	C₂²⋊Dic₄₇	—	2	2	no	—
201	C₂²⋊Dic₄₇	—	2	2	no	—
202	C₂²⋊Dic₄₇	—	4	1	no	—
203	(C₂×D₄₇)⋊C₄	—	2	8	no	—
204	C₄⋊Dic₄₇	—	2	2	no	—
205	C₄⋊Dic₄₇	—	2	2	no	—
206	C₄⋊Dic₄₇	—	2	2	no	—
207	C₄⋊Dic₄₇	—	4	1	no	—
208	Dic₄₇⋊C₄	—	2	8	no	—
209	C₄×Dic₄₇	—	2	2	no	—
210	C₄×Dic₄₇	—	2	8	no	—
211	C₄×Dic₄₇	—	2	2	no	—
212	C₄×Dic₄₇	—	4	1	no	—
213	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
214	#10625329	—	2	2	no	—
215	#10625329	—	2	2	no	—
216	#10625329	—	4	1	no	—
217	#10625329	—	4	1	no	—
218	C₂×C₄₇⋊C₈	—	2	2	no	—
219	C₂×C₄₇⋊C₈	—	4	1	no	—
220	C₂×C₄₇⋊C₈	—	4	1	no	—
221	C₂³×C₄₇	—	4	2	no	—
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×C₄₇	#123	1	1	yes	characteristic
225	C₂³×C₄₇	#123	1	1	yes	characteristic
226	C₂³×C₄₇	#123	1	1	yes	characteristic
227	C₂³×C₄₇	#123	1	1	yes	characteristic
228	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂²×D₄₇	—	2	2	no	—
230	C₂²×D₄₇	—	2	2	no	—
231	C₂²×D₄₇	—	4	4	no	—
232	C₂²×D₄₇	C₂×C₂²⋊C₄	1	4	yes	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	4	4	no	—
237	C₂×C₄×C₄₇	—	4	4	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	4	2	no	—
240	C₂×C₄×C₄₇	—	8	2	no	—
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
248	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
249	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
250	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
251	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
253	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
254	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
255	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
256	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
257	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
258	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
261	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
262	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
269	C₂²⋊D₄₇	—	2	4	no	—
270	C₂²⋊D₄₇	—	2	4	no	—
271	C₂²⋊D₄₇	—	2	4	no	—
272	C₂²⋊D₄₇	—	2	4	no	—
273	C₂×Dic₄₇	—	2	2	no	—
274	C₂×Dic₄₇	—	2	2	no	—
275	C₂×Dic₄₇	—	2	4	no	—
276	C₂×Dic₄₇	—	4	4	no	—
277	C₂×Dic₄₇	—	4	2	no	—
278	C₂×Dic₄₇	—	8	2	no	—
279	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
280	D₁₈₈	—	2	2	no	—
281	D₁₈₈	—	2	2	no	—
282	D₁₈₈	—	2	2	no	—
283	D₁₈₈	—	2	2	no	—
284	C₄×D₄₇	—	2	4	no	—
285	C₄×D₄₇	—	2	4	no	—
286	C₄×D₄₇	—	2	4	no	—
287	C₄×D₄₇	—	2	4	no	—
288	C₄×D₄₇	—	4	16	no	—
289	Dic₉₄	—	2	2	no	—
290	Dic₉₄	—	2	2	no	—
291	Dic₉₄	—	2	2	no	—
292	Dic₉₄	—	2	2	no	—
293	C₈×C₄₇	—	4	2	no	—
294	C₄₇⋊C₈	—	4	2	no	—
295	C₂×#1827	—	47	1	no	maximal, Sylow
296	C₂²×C₄₇	—	2	2	no	—
297	C₂²×C₄₇	—	2	2	no	—
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	4	1	no	—
300	C₂²×C₄₇	—	4	1	no	—
301	C₂²×C₄₇	—	4	1	no	—
302	C₂²×C₄₇	—	4	1	no	—
303	C₂²×C₄₇	#381	1	1	yes	characteristic
304	C₂²×C₄₇	#381	1	1	yes	characteristic
305	C₂²×C₄₇	#381	1	1	yes	characteristic
306	C₂²×C₄₇	#381	1	1	yes	characteristic
307	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
309	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
310	C₂×D₄₇	—	2	4	no	—
311	C₂×D₄₇	—	4	4	no	—
312	C₂×D₄₇	—	4	4	no	—
313	C₂×D₄₇	—	4	4	no	—
314	C₄×C₄₇	—	2	4	no	—
315	C₄×C₄₇	—	4	2	no	—
316	C₄×C₄₇	—	8	2	no	—
317	C₄×C₄₇	#381	1	1	yes	characteristic
318	C₄×C₄₇	#381	1	1	yes	characteristic
319	C₄×C₄₇	#381	1	1	yes	characteristic
320	C₄×C₄₇	#381	1	1	yes	characteristic
321	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
322	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
323	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
324	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
325	Dic₄₇	—	2	4	no	—
326	Dic₄₇	—	4	4	no	—
327	Dic₄₇	—	8	2	no	—
328	C₂×C₄×#41	—	47	1	no	—
329	C₂×#413	—	47	1	no	—
330	C₂×#410	—	47	1	no	—
331	#1827	—	47	8	no	—
332	C₂×#339	—	47	1	no	—
333	C₂×#339	D₄₇	1	1	yes	characteristic, complemented
334	C₂×H(3,ℤ/4)	—	47	1	no	—
335	C₂×H(3,ℤ/4)	—	47	1	no	—
336	C₂×C₄₇	—	2	1	no	—
337	C₂×C₄₇	—	2	1	no	—
338	C₂×C₄₇	—	2	1	no	—
339	C₂×C₄₇	—	2	1	no	—
340	C₂×C₄₇	—	2	1	no	—
341	C₂×C₄₇	—	2	1	no	—
342	C₂×C₄₇	#1827	1	2	yes	complemented
343	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
344	D₄₇	—	4	4	no	—
345	C₂²×#41	—	47	1	no	—
346	C₂²×M₁₆	—	47	1	no	—
347	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
348	C₄×#41	—	47	4	no	—
349	C₄×#41	—	47	4	no	—
350	C₄×#41	—	94	2	no	—
351	C₄×#41	—	94	2	no	—
352	C₂×C₄×Q₈	—	94	1	no	—
353	C₂×C₄×D₄	—	94	1	no	—
354	C₂×C₄×D₄	—	94	2	no	—
355	C₂×#117	—	47	1	no	—
356	C₂×#117	—	47	2	no	—
357	C₂×#117	—	47	1	no	—
358	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
359	C₂²×C₄²	—	47	2	no	—
360	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
361	#413	—	47	4	no	—
362	#413	—	94	2	no	—
363	C₂×#101	—	94	1	no	—
364	C₂×#100	—	94	1	no	—
365	#410	—	47	4	no	—
366	#410	—	94	2	no	—
367	C₂×#99	—	94	2	no	—
368	#339	—	47	4	no	—
369	#339	C₂×D₄₇	1	4	yes	complemented
370	H(3,ℤ/4)	—	47	4	no	—
371	H(3,ℤ/4)	—	47	4	no	—
372	C₄₇	C₂×#1827	1	1	yes	characteristic, complemented, Sylow
373	C₂×#41	—	47	2	no	—
374	C₂×#41	—	47	2	no	—
375	C₂×#41	—	47	2	no	—
376	C₂×#41	—	47	2	no	—
377	C₂×#41	—	94	1	no	—
378	C₂×#41	—	94	1	no	—
379	C₂×#41	—	94	1	no	—
380	C₂×#41	—	94	1	no	—
381	C₂×#41	—	94	1	no	—
382	C₂×#41	—	94	1	no	—
383	C₂×#41	—	94	1	no	—
384	C₂×#41	—	94	1	no	—
385	C₂²×Q₈	—	47	1	no	—
386	C₂²×D₄	—	47	2	no	—
387	C₂²×D₄	—	47	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	47	2	no	—
390	C₂³×C₄	—	94	2	no	—
391	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	47	2	no	—
398	C₂×M₁₆	—	94	1	no	—
399	C₂×M₁₆	—	94	1	no	—
400	C₂×M₁₆	—	94	1	no	—
401	C₂×M₁₆	—	94	1	no	—
402	C₂×M₁₆	—	94	1	no	—
403	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	94	1	no	—
406	C₄×Q₈	—	94	4	no	—
407	C₄×Q₈	—	94	4	no	—
408	C₄×D₄	—	94	4	no	—
409	C₄×D₄	—	94	4	no	—
410	C₄×D₄	—	94	8	no	—
411	C₄×D₄	—	94	8	no	—
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	47	2	no	—
416	#117	—	47	2	no	—
417	#117	—	47	8	no	—
418	#117	—	47	2	no	—
419	#117	—	94	4	no	—
420	#117	—	94	1	no	—
421	#117	—	94	1	no	—
422	#117	—	94	1	no	—
423	#117	—	94	1	no	—
424	#117	—	94	1	no	—
425	#117	C₂²×D₄₇	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	94	2	no	—
428	C₂×C₄⋊C₄	—	94	1	no	—
429	C₂×C₄⋊C₄	—	94	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	94	2	no	—
432	C₂×C₂²⋊C₄	—	94	1	no	—
433	C₂×C₂²⋊C₄	—	94	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	47	2	no	—
439	C₂×C₄²	—	47	8	no	—
440	C₂×C₄²	—	94	4	no	—
441	C₂×C₄²	—	94	2	no	—
442	C₂×C₄²	—	94	1	no	—
443	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
444	C₂×C₄²	C₄×D₄₇	1	2	yes	—
445	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
446	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
447	#101	—	94	4	no	—
448	#100	—	94	4	no	—
449	#99	—	94	8	no	—
450	C₂⁴	—	47	2	no	—
451	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
452	#41	—	94	2	no	—
453	#41	—	94	2	no	—
454	#41	—	94	2	no	—
455	#41	—	94	2	no	—
456	#41	—	94	2	no	—
457	#41	—	94	2	no	—
458	#41	—	94	2	no	—
459	#41	—	94	2	no	—
460	#41	—	94	2	no	—
461	#41	—	94	2	no	—
462	#41	—	94	2	no	—
463	#41	—	94	2	no	—
464	#41	—	94	2	no	—
465	#41	—	94	2	no	—
466	#41	—	94	2	no	—
467	#41	—	94	2	no	—
468	C₂×Q₈	—	47	2	no	—
469	C₂×Q₈	—	47	2	no	—
470	C₂×Q₈	—	94	1	no	—
471	C₂×Q₈	—	94	1	no	—
472	C₂×Q₈	—	94	1	no	—
473	C₂×Q₈	—	94	1	no	—
474	C₂×D₄	—	47	4	no	—
475	C₂×D₄	—	47	4	no	—
476	C₂×D₄	—	47	2	no	—
477	C₂×D₄	—	47	2	no	—
478	C₂×D₄	—	94	2	no	—
479	C₂×D₄	—	94	2	no	—
480	C₂×D₄	—	94	2	no	—
481	C₂×D₄	—	94	2	no	—
482	C₂×D₄	—	94	1	no	—
483	C₂×D₄	—	94	1	no	—
484	C₂×D₄	—	94	1	no	—
485	C₂×D₄	—	94	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	—	47	2	no	—
493	C₂²×C₄	—	47	4	no	—
494	C₂²×C₄	—	47	4	no	—
495	C₂²×C₄	—	94	8	no	—
496	C₂²×C₄	—	94	2	no	—
497	C₂²×C₄	—	94	2	no	—
498	C₂²×C₄	—	94	2	no	—
499	C₂²×C₄	—	94	2	no	—
500	C₂²×C₄	—	94	2	no	—
501	C₂²×C₄	—	188	8	no	—
502	C₂²×C₄	—	188	1	no	—
503	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
505	C₂²×C₄	#10625350	1	1	yes	characteristic
506	C₂²×C₄	#10625350	1	1	yes	characteristic
507	C₂²×C₄	#10625350	1	1	yes	characteristic
508	C₂²×C₄	#10625350	1	1	yes	characteristic
509	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
510	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
511	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
512	C₂²×C₄	#10625352	1	1	yes	characteristic
513	C₂²×C₄	#10625352	1	1	yes	characteristic
514	C₂²×C₄	#10625354	1	1	yes	characteristic
515	C₂²×C₄	#10625354	1	1	yes	characteristic
516	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
517	M₁₆	—	2	2	no	—
518	M₁₆	—	2	2	no	—
519	M₁₆	—	4	1	no	—
520	M₁₆	—	4	1	no	—
521	M₁₆	—	94	2	no	—
522	M₁₆	—	94	2	no	—
523	M₁₆	—	188	1	no	—
524	M₁₆	—	188	1	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	4	1	no	—
527	C₂×C₈	—	4	1	no	—
528	C₂×C₈	—	94	2	no	—
529	C₂×C₈	—	188	1	no	—
530	C₂×C₈	—	188	1	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₄⋊C₄	—	94	8	no	—
534	C₄⋊C₄	—	94	2	no	—
535	C₄⋊C₄	—	94	2	no	—
536	C₄⋊C₄	—	94	2	no	—
537	C₄⋊C₄	—	188	1	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	94	8	no	—
541	C₂²⋊C₄	—	94	2	no	—
542	C₂²⋊C₄	—	94	2	no	—
543	C₂²⋊C₄	—	94	2	no	—
544	C₂²⋊C₄	—	188	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	4	1	no	—
551	C₄²	—	47	4	no	—
552	C₄²	—	94	8	no	—
553	C₄²	—	94	2	no	—
554	C₄²	—	94	2	no	—
555	C₄²	—	188	1	no	—
556	C₄²	C₂×C₄×D₄₇	1	2	yes	—
557	C₄²	C₂×C₄×D₄₇	1	2	yes	—
558	C₂³	—	4	2	no	—
559	C₂³	—	47	4	no	—
560	C₂³	—	94	2	no	—
561	C₂³	—	94	2	no	—
562	C₂³	—	188	4	no	—
563	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
564	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
565	C₂³	#13094006	1	1	yes	characteristic
566	C₂³	#13094006	1	1	yes	characteristic
567	C₂³	#13094009	1	1	yes	characteristic
568	C₂³	#13094009	1	1	yes	characteristic
569	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
570	Q₈	—	94	2	no	—
571	Q₈	—	94	2	no	—
572	Q₈	—	94	2	no	—
573	Q₈	—	94	2	no	—
574	D₄	—	94	4	no	—
575	D₄	—	94	4	no	—
576	D₄	—	94	4	no	—
577	D₄	—	94	4	no	—
578	D₄	—	94	2	no	—
579	D₄	—	94	2	no	—
580	D₄	—	94	2	no	—
581	D₄	—	94	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	—	47	4	no	—
591	C₂×C₄	—	94	2	no	—
592	C₂×C₄	—	94	2	no	—
593	C₂×C₄	—	94	4	no	—
594	C₂×C₄	—	94	4	no	—
595	C₂×C₄	—	94	4	no	—
596	C₂×C₄	—	94	4	no	—
597	C₂×C₄	—	94	4	no	—
598	C₂×C₄	—	376	2	no	—
599	C₂×C₄	—	188	16	no	—
600	C₂×C₄	—	188	2	no	—
601	C₂×C₄	—	188	4	no	—
602	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
603	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
604	C₂×C₄	#13093981	1	1	yes	characteristic
605	C₂×C₄	#13093981	1	1	yes	characteristic
606	C₂×C₄	#13093981	1	1	yes	characteristic
607	C₂×C₄	#13093981	1	1	yes	characteristic
608	C₂×C₄	#13093982	1	1	yes	characteristic
609	C₂×C₄	#13093982	1	1	yes	characteristic
610	C₂×C₄	#13093982	1	1	yes	characteristic
611	C₂×C₄	#13093982	1	1	yes	characteristic
612	C₂×C₄	#13094006	1	1	yes	characteristic
613	C₂×C₄	#13094006	1	1	yes	characteristic
614	C₂×C₄	#13094006	1	1	yes	characteristic
615	C₂×C₄	#13094006	1	1	yes	characteristic
616	C₂×C₄	#13094006	1	1	yes	characteristic
617	C₂×C₄	#13094006	1	1	yes	characteristic
618	C₂×C₄	#13094009	1	1	yes	characteristic
619	C₂×C₄	#13094009	1	1	yes	characteristic
620	C₂×C₄	#13094009	1	1	yes	characteristic
621	C₂×C₄	#13094009	1	1	yes	characteristic
622	C₂×C₄	#13094009	1	1	yes	characteristic
623	C₂×C₄	#13094009	1	1	yes	characteristic
624	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
625	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
626	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
627	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
628	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
629	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
630	C₈	—	4	2	no	—
631	C₈	—	188	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	94	4	no	—
640	C₂²	—	188	4	no	—
641	C₂²	—	188	4	no	—
642	C₂²	—	188	4	no	—
643	C₂²	#15688985	1	1	yes	characteristic
644	C₂²	#15688985	1	1	yes	characteristic
645	C₂²	#15688985	1	1	yes	characteristic
646	C₂²	#15688985	1	1	yes	characteristic
647	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
648	C₂²	C₂×#13094006	1	1	yes	characteristic
649	C₂²	C₂×#13094009	1	1	yes	characteristic
650	C₄	—	2	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	8	2	no	—
653	C₄	—	94	4	no	—
654	C₄	—	376	2	no	—
655	C₄	—	188	4	no	—
656	C₄	#15688985	1	1	yes	characteristic
657	C₄	#15688985	1	1	yes	characteristic
658	C₄	#15688985	1	1	yes	characteristic
659	C₄	#15688985	1	1	yes	characteristic
660	C₄	C₂×#13093981	1	1	yes	characteristic
661	C₄	C₂×#13093982	1	1	yes	characteristic
662	C₄	C₂×#13094006	1	1	yes	characteristic
663	C₄	C₂×#13094009	1	1	yes	characteristic
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	2	1	no	—
669	C₂	—	2	1	no	—
670	C₂	—	188	4	no	—
671	C₂	#20243491	1	2	yes	direct product factor
672	C₂	C₂×#15688985	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093982
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#339	C₂
socle	C₂²×C₄₇	#381
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#339	D₄₇
hypocenter	C₄₇	C₂×#1827
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. #20243491	C₂	direct (N × H)
5. C₂×#15688883	C₂	semidirect
6. C₂×#15688880	C₂	semidirect
7. C₂×#15688879	C₂	semidirect
8. C₂×C₄₇×#339	C₂	semidirect
13. C₄×#10625350	C₄	semidirect
20. C₂×#13093981	C₄	semidirect
21. C₂×C₄²×D₄₇	C₄	semidirect
29. #15688883	C₂²	semidirect
30. #15688880	C₂²	semidirect
31. #15688879	C₂²	semidirect
35. C₄₇×#339	C₂²	semidirect
75. #13093981	C₂×C₄	semidirect
86. C₄²×D₄₇	C₂×C₄	semidirect
333. C₂×#339	D₄₇	semidirect
342. C₂×C₄₇	#1827	semidirect
369. #339	C₂×D₄₇	semidirect
372. C₄₇	C₂×#1827	semidirect
671. C₂	#20243491	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×C₄×#10625350	2
C₂×#15689105	2
C₂×#15689096	2
#20243491	2
C₂×#15688883	2
C₂×#15688880	2
C₂×#15688879	2
C₂×C₄₇×#339	2
C₂×#1827	47

Subgroups — C2×#20243491 #26216121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243491 #26216121