Subgroups — C₂×#20245124 #26369220

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093964	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245124	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688933	C₂	1	4	yes	maximal, complemented
5	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	—	2	1	no	—
7	C₂×#13093964	—	2	1	no	—
8	C₂×#13093964	—	2	2	no	—
9	C₂×#13093964	C₂²	1	2	yes	complemented
10	C₂×#13093964	C₂²	1	4	yes	complemented
11	C₂²×C₄₇⋊C₁₆	—	2	1	no	—
12	#15689161	—	2	2	no	—
13	#15689161	C₂²	1	4	yes	complemented
14	C₂×#13093958	—	2	1	no	—
15	C₂×#13093956	C₂²	1	2	yes	complemented
16	#15688933	C₂²	1	16	yes	complemented
17	C₂²×#41×C₄₇	—	2	1	no	—
18	C₂×#135×C₄₇	—	2	1	no	—
19	C₂×#135×C₄₇	—	2	2	no	—
20	C₂×#135×C₄₇	—	2	1	no	—
21	C₂×#135×C₄₇	—	2	2	no	—
22	C₂×#135×C₄₇	C₄	1	2	yes	complemented
23	C₂×#135×C₄₇	C₄	1	4	yes	complemented
24	C₂×#135×C₄₇	C₂²	1	2	yes	—
25	C₂×#135×C₄₇	C₂²	1	4	yes	—
26	C₂²×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
27	C₂²×SD₁₆×C₄₇	—	2	1	no	—
28	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
29	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	#13093983	—	2	4	no	—
31	#13093983	—	4	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₂²⋊Dic₄₇	—	4	1	no	—
34	C₂×C₄×Dic₄₇	—	4	1	no	—
35	#13093964	—	2	4	no	—
36	#13093964	—	2	2	no	—
37	#13093964	C₂³	1	4	yes	complemented
38	C₂×C₄₇⋊C₁₆	—	2	2	no	—
39	C₂×C₄₇⋊C₁₆	—	2	4	no	—
40	#13093958	—	2	4	no	—
41	#13093956	—	2	2	no	—
42	#13093956	C₂³	1	4	yes	complemented
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	4	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	4	no	—
47	C₂×#41×C₄₇	—	4	1	no	—
48	C₂×#41×C₄₇	—	4	2	no	—
49	C₂×#41×C₄₇	—	4	1	no	—
50	C₂×#41×C₄₇	—	4	2	no	—
51	C₂²×Q₈×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	4	1	no	—
54	C₂³×C₄×C₄₇	—	4	1	no	—
55	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
56	#135×C₄₇	—	2	4	no	—
57	#135×C₄₇	—	2	4	no	—
58	#135×C₄₇	—	2	4	no	—
59	#135×C₄₇	—	2	2	no	—
60	#135×C₄₇	—	2	4	no	—
61	#135×C₄₇	—	2	4	no	—
62	#135×C₄₇	—	2	2	no	—
63	#135×C₄₇	C₂×C₄	1	4	yes	—
64	#135×C₄₇	C₂×C₄	1	8	yes	complemented
65	#135×C₄₇	C₂³	1	4	yes	—
66	C₂×Q₁₆×C₄₇	—	2	2	no	—
67	C₂×Q₁₆×C₄₇	—	2	1	no	—
68	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
70	C₂×SD₁₆×C₄₇	—	2	4	no	—
71	C₂×SD₁₆×C₄₇	—	2	2	no	—
72	C₂×SD₁₆×C₄₇	—	2	2	no	—
73	C₂×SD₁₆×C₄₇	—	2	4	no	—
74	C₂×D₈×C₄₇	—	2	2	no	—
75	C₂×D₈×C₄₇	—	2	1	no	—
76	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	D₄	1	2	yes	—
83	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	D₄	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
88	C₂⁴×C₄₇	—	4	1	no	—
89	C₂⁴×C₄₇	D₈	1	1	yes	characteristic
90	#41×C₄₇	—	2	4	no	—
91	#41×C₄₇	—	2	8	no	—
92	#41×C₄₇	—	2	4	no	—
93	#41×C₄₇	—	4	4	no	—
94	#41×C₄₇	—	4	4	no	—
95	#41×C₄₇	—	4	4	no	—
96	#41×C₄₇	—	4	4	no	—
97	#41×C₄₇	—	4	2	no	—
98	#41×C₄₇	—	4	2	no	—
99	#41×C₄₇	—	4	4	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	4	no	—
102	C₂×Q₈×C₄₇	—	4	2	no	—
103	C₂×Q₈×C₄₇	—	4	1	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	4	no	—
106	C₂×D₄×C₄₇	—	4	2	no	—
107	C₂×D₄×C₄₇	—	4	4	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	2	no	—
111	C₂×D₄×C₄₇	—	4	1	no	—
112	C₂²×C₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	—	4	4	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	D₈	1	2	yes	—
122	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×Dic₄₇	—	4	2	no	—
128	Q₁₆×C₄₇	—	2	2	no	—
129	Q₁₆×C₄₇	—	2	4	no	—
130	Q₁₆×C₄₇	C₂²×C₄	1	4	yes	—
131	SD₁₆×C₄₇	—	2	4	no	—
132	SD₁₆×C₄₇	—	2	8	no	—
133	SD₁₆×C₄₇	—	2	4	no	—
134	D₈×C₄₇	—	2	2	no	—
135	D₈×C₄₇	—	2	4	no	—
136	D₈×C₄₇	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
141	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²⋊Dic₄₇	—	4	4	no	—
156	C₄⋊Dic₄₇	—	2	4	no	—
157	C₄⋊Dic₄₇	—	4	2	no	—
158	C₄×Dic₄₇	—	4	4	no	—
159	C₄₇⋊C₁₆	—	2	4	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	8	4	no	—
164	C₂³×C₄₇	#102	1	1	yes	characteristic
165	C₂³×C₄₇	#102	1	1	yes	characteristic
166	C₂³×C₄₇	#102	1	2	yes	—
167	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
168	C₂³×C₄₇	C₂×D₈	1	2	yes	—
169	Q₈×C₄₇	—	2	4	no	—
170	Q₈×C₄₇	—	4	2	no	—
171	Q₈×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	4	4	no	—
174	D₄×C₄₇	—	4	4	no	—
175	D₄×C₄₇	—	4	8	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	—	4	4	no	—
182	C₂×C₄×C₄₇	—	4	8	no	—
183	C₂×C₄×C₄₇	#102	1	2	yes	—
184	C₂×C₄×C₄₇	#102	1	2	yes	—
185	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
186	C₂×C₄×C₄₇	#102	1	2	yes	—
187	C₂×C₄×C₄₇	#102	1	2	yes	—
188	C₂×C₄×C₄₇	#102	1	2	yes	—
189	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
195	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
197	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×Dic₄₇	—	4	4	no	—
202	C₂×Dic₄₇	—	8	4	no	—
203	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
205	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
207	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
208	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×#2145	—	47	1	no	maximal, Sylow
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	2	2	no	—
212	C₂²×C₄₇	—	2	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	—	8	8	no	—
217	C₂²×C₄₇	—	8	4	no	—
218	C₂²×C₄₇	C₂×#102	1	2	yes	—
219	C₂²×C₄₇	C₂×#102	1	2	yes	—
220	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
222	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
223	C₄×C₄₇	—	4	4	no	—
224	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
225	C₄×C₄₇	C₂×#102	1	2	yes	—
226	C₄×C₄₇	C₂×#102	1	2	yes	—
227	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
228	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
230	Dic₄₇	—	8	4	no	—
231	C₂²×#135	D₄₇	1	1	yes	characteristic
232	C₂²×M₃₂	—	47	1	no	—
233	C₂×#427	—	47	1	no	—
234	#2145	—	47	8	no	—
235	C₂×#360	—	47	4	no	—
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	2	no	—
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	—	2	2	no	—
240	C₂×C₄₇	—	8	4	no	—
241	C₂×C₄₇	#2145	1	2	yes	complemented
242	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
243	C₂²×#41	—	2	1	no	—
244	C₂×#135	—	2	1	no	—
245	C₂×#135	—	2	2	no	—
246	C₂×#135	—	2	1	no	—
247	C₂×#135	—	2	2	no	—
248	C₂×#135	Dic₄₇	1	2	yes	complemented
249	C₂×#135	Dic₄₇	1	4	yes	complemented
250	C₂×#135	C₂×D₄₇	1	2	yes	—
251	C₂×#135	C₂×D₄₇	1	4	yes	—
252	C₂²×Q₁₆	Dic₄₇	1	1	yes	characteristic, complemented
253	C₂²×SD₁₆	—	2	1	no	—
254	C₂²×D₈	Dic₄₇	1	1	yes	characteristic, complemented
255	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×#117	—	94	1	no	—
257	C₂×M₃₂	—	47	2	no	—
258	C₂×M₃₂	—	47	4	no	—
259	C₂×M₃₂	—	94	1	no	—
260	C₂×M₃₂	—	94	2	no	—
261	C₂²×C₁₆	—	94	1	no	—
262	#427	—	47	4	no	—
263	#427	—	94	2	no	—
264	C₂×#107	—	94	1	no	—
265	C₂×#106	—	47	2	no	—
266	#360	—	47	16	no	—
267	C₄₇	C₂×#2145	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	4	2	no	—
273	C₂×#41	—	4	1	no	—
274	C₂×#41	—	4	1	no	—
275	C₂×#41	—	4	2	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	4	1	no	—
279	C₂³×C₄	—	4	1	no	—
280	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
281	#135	—	2	4	no	—
282	#135	—	2	4	no	—
283	#135	—	2	4	no	—
284	#135	—	2	2	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	2	no	—
288	#135	C₂×Dic₄₇	1	4	yes	—
289	#135	C₂×Dic₄₇	1	8	yes	complemented
290	#135	C₂²×D₄₇	1	4	yes	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×Q₁₆	—	2	1	no	—
293	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	—
294	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
302	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
303	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
306	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
308	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
310	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
311	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
313	#117	—	94	4	no	—
314	#117	—	188	2	no	—
315	C₂×C₄⋊C₄	—	94	2	no	—
316	C₂×C₂²⋊C₄	—	188	1	no	—
317	C₂×C₄²	—	188	1	no	—
318	M₃₂	—	47	4	no	—
319	M₃₂	—	94	4	no	—
320	M₃₂	—	94	2	no	—
321	C₂×C₁₆	—	94	2	no	—
322	C₂×C₁₆	—	94	4	no	—
323	#107	—	94	4	no	—
324	#106	—	47	4	no	—
325	#106	—	94	2	no	—
326	C₂⁴	—	4	1	no	—
327	C₂⁴	#10625334	1	1	yes	characteristic
328	#41	—	2	4	no	—
329	#41	—	2	8	no	—
330	#41	—	2	4	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	#41	—	4	4	no	—
334	#41	—	4	4	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	4	4	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	4	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	188	2	no	—
356	C₂²×C₄	#10625334	1	2	yes	—
357	C₂²×C₄	#10625334	1	1	yes	characteristic
358	C₂²×C₄	#10625335	1	1	yes	characteristic
359	C₂²×C₄	#10625335	1	2	yes	—
360	C₂²×C₄	#10625335	1	1	yes	characteristic
361	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
363	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
366	Q₁₆	—	2	2	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	C₂²×Dic₄₇	1	4	yes	—
369	SD₁₆	—	2	4	no	—
370	SD₁₆	—	2	8	no	—
371	SD₁₆	—	2	4	no	—
372	D₈	—	2	2	no	—
373	D₈	—	2	4	no	—
374	D₈	C₂²×Dic₄₇	1	4	yes	—
375	C₂×C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
376	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
377	C₂×C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
378	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
379	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
380	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
381	C₂×C₈	C₂²⋊Dic₄₇	1	2	yes	—
382	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
383	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
384	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
385	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
386	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
388	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
390	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
391	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	188	2	no	—
395	C₂²⋊C₄	—	188	4	no	—
396	C₄²	—	188	4	no	—
397	C₁₆	—	94	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	8	4	no	—
402	C₂³	#13093945	1	1	yes	characteristic
403	C₂³	#13093945	1	1	yes	characteristic
404	C₂³	#13093945	1	2	yes	—
405	C₂³	C₂×#10625334	1	1	yes	characteristic
406	C₂³	C₂×#10625334	1	2	yes	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	8	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	376	4	no	—
422	C₂×C₄	—	188	4	no	—
423	C₂×C₄	#13093945	1	2	yes	—
424	C₂×C₄	#13093945	1	2	yes	—
425	C₂×C₄	#13093945	1	1	yes	characteristic
426	C₂×C₄	#13093945	1	2	yes	—
427	C₂×C₄	#13093945	1	2	yes	—
428	C₂×C₄	#13093945	1	2	yes	—
429	C₂×C₄	#13093945	1	1	yes	characteristic
430	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
434	C₂×C₄	C₂×#10625334	1	2	yes	—
435	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
436	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
437	C₂×C₄	C₂×#10625335	1	2	yes	—
438	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
439	C₂×C₄	C₂×#10625335	1	2	yes	—
440	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
441	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
442	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
443	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
444	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
445	C₈	C₂³×Dic₄₇	1	1	yes	characteristic
446	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	8	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×#13093945	1	2	yes	—
456	C₂²	C₂×#13093945	1	2	yes	—
457	C₂²	C₂×#13093945	1	1	yes	characteristic
458	C₂²	C₂×#13093945	1	1	yes	characteristic
459	C₂²	C₂²×#10625334	1	1	yes	characteristic
460	C₄	—	4	4	no	—
461	C₄	—	376	4	no	—
462	C₄	C₂×#13093945	1	1	yes	characteristic
463	C₄	C₂×#13093945	1	2	yes	—
464	C₄	C₂×#13093945	1	2	yes	—
465	C₄	C₂×#13093945	1	1	yes	characteristic
466	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₄	C₂²×#10625335	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	2	no	—
472	C₂	—	8	4	no	—
473	C₂	#20245124	1	2	yes	direct product factor
474	C₂	C₂²×#13093945	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093945
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#102
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	C₂×#2145
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093964	C₂	semidirect
2. C₂×#15689161	C₂	semidirect
3. #20245124	C₂	direct (N × H)
4. C₂×#15688933	C₂	semidirect
9. C₂×#13093964	C₂²	semidirect
10. C₂×#13093964	C₂²	semidirect
13. #15689161	C₂²	semidirect
15. C₂×#13093956	C₂²	semidirect
16. #15688933	C₂²	semidirect
22. C₂×#135×C₄₇	C₄	semidirect
23. C₂×#135×C₄₇	C₄	semidirect
26. C₂²×Q₁₆×C₄₇	C₄	semidirect
28. C₂²×D₈×C₄₇	C₄	semidirect
37. #13093964	C₂³	semidirect
42. #13093956	C₂³	semidirect
64. #135×C₄₇	C₂×C₄	semidirect
69. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
77. C₂×D₈×C₄₇	C₂×C₄	semidirect
241. C₂×C₄₇	#2145	semidirect
248. C₂×#135	Dic₄₇	semidirect
249. C₂×#135	Dic₄₇	semidirect
252. C₂²×Q₁₆	Dic₄₇	semidirect
254. C₂²×D₈	Dic₄₇	semidirect
267. C₄₇	C₂×#2145	semidirect
289. #135	C₂×Dic₄₇	semidirect
294. C₂×Q₁₆	C₂×Dic₄₇	semidirect
302. C₂×D₈	C₂×Dic₄₇	semidirect
473. C₂	#20245124	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×#13093964	2
C₂×#15689161	2
#20245124	2
C₂×#15688933	2
C₂²×#135×C₄₇	2
C₂×#2145	47

Subgroups — C2×#20245124 #26369220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245124 #26369220