Subgroups — C₂×#20243191 #26213979

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094031	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689097	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689081	C₂	1	2	yes	maximal, complemented
4	#20243191	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688895	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#413	C₂	1	1	yes	maximal, characteristic
7	C₂×#13094031	—	2	2	no	—
8	C₂×#13094031	—	2	2	no	—
9	C₂×#13094031	—	2	4	no	—
10	C₂×#13094031	C₄	1	4	yes	complemented
11	C₂×#13094031	C₂²	1	4	yes	—
12	C₂²×#10625329	C₄	1	2	yes	complemented
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₄	1	2	yes	complemented
15	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×#13093983	C₂²	1	2	yes	—
17	#15689097	C₄	1	4	yes	—
18	#15689097	C₂²	1	4	yes	—
19	C₂×#13093939	C₄	1	4	yes	—
20	#15689081	—	2	4	no	—
21	#15689081	C₂²	1	8	yes	complemented
22	C₂×#13093934	—	2	2	no	—
23	C₂×C₈×Dic₄₇	—	2	2	no	—
24	#15688895	C₂²	1	8	yes	complemented
25	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
27	C₄₇×#413	C₄	1	4	yes	complemented
28	C₄₇×#413	C₂²	1	4	yes	—
29	C₂×#101×C₄₇	C₄	1	2	yes	complemented
30	C₂×#100×C₄₇	C₄	1	2	yes	complemented
31	#13094031	—	2	8	no	—
32	#13094031	—	2	8	no	—
33	#13094031	—	2	8	no	—
34	#13094031	—	2	8	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	4	no	—
38	C₂×#10625329	—	2	4	no	—
39	C₂×#10625329	C₂×C₄	1	2	yes	—
40	C₂×#10625329	C₂×C₄	1	8	yes	complemented
41	C₂×#10625329	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	—	2	4	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
50	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
52	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	#13093983	—	2	2	no	—
55	#13093983	—	2	2	no	—
56	#13093983	C₂×C₄	1	4	yes	—
57	#13093983	C₂³	1	4	yes	—
58	C₂×C₄⋊Dic₄₇	—	2	2	no	—
59	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	#13093939	C₂×C₄	1	16	yes	—
62	#13093934	—	2	8	no	—
63	C₈×Dic₄₇	—	2	8	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	—	2	2	no	—
66	C₂×#41×C₄₇	—	2	2	no	—
67	C₂×#41×C₄₇	—	2	2	no	—
68	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×#41×C₄₇	C₂³	1	2	yes	—
72	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₄₇	—	2	2	no	—
78	C₂×M₁₆×C₄₇	—	2	2	no	—
79	C₂×M₁₆×C₄₇	—	2	2	no	—
80	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
82	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
83	C₂²×C₈×C₄₇	—	2	2	no	—
84	#101×C₄₇	C₂×C₄	1	8	yes	complemented
85	#100×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₂⁴×C₄₇	C₄²	1	2	yes	—
87	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	#41×C₄₇	—	2	4	no	—
89	#41×C₄₇	—	2	4	no	—
90	#41×C₄₇	—	2	4	no	—
91	#41×C₄₇	—	2	4	no	—
92	#41×C₄₇	—	2	4	no	—
93	#41×C₄₇	—	2	4	no	—
94	#41×C₄₇	—	2	4	no	—
95	#41×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
99	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	C₄²	1	4	yes	—
105	C₂×D₄×C₄₇	C₄²	1	2	yes	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
113	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₇	#41	1	2	yes	—
123	C₂²×C₄×C₄₇	#41	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	—	2	4	no	—
126	M₁₆×C₄₇	—	2	4	no	—
127	M₁₆×C₄₇	—	2	4	no	—
128	M₁₆×C₄₇	—	2	4	no	—
129	M₁₆×C₄₇	C₂²×C₄	1	8	yes	—
130	C₂×C₈×C₄₇	—	2	4	no	—
131	C₂×C₈×C₄₇	—	2	4	no	—
132	C₂×C₈×C₄₇	—	2	4	no	—
133	C₂²⋊Dic₄₇	—	2	4	no	—
134	C₂²⋊Dic₄₇	C₂²×C₄	1	8	yes	—
135	C₄⋊Dic₄₇	—	2	4	no	—
136	C₄⋊Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	2	4	no	—
139	#10625329	—	2	4	no	—
140	#10625329	—	2	4	no	—
141	#10625329	—	2	16	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	8	no	—
145	C₂×C₄₇⋊C₈	—	2	8	no	—
146	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
147	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
152	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
154	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
163	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
164	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
165	C₂³×C₄₇	C₄×D₄	1	2	yes	—
166	C₂³×C₄₇	C₄×D₄	1	2	yes	—
167	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	Q₈×C₄₇	—	2	4	no	—
169	Q₈×C₄₇	—	2	4	no	—
170	D₄×C₄₇	—	2	8	no	—
171	D₄×C₄₇	—	2	8	no	—
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
181	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
187	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#117	1	2	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
199	C₂×Dic₄₇	—	2	8	no	—
200	C₂×Dic₄₇	—	4	8	no	—
201	C₈×C₄₇	—	2	8	no	—
202	C₄₇⋊C₈	—	2	4	no	—
203	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
204	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
205	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂×#1757	—	47	1	no	maximal, Sylow
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	4	no	—
210	C₂²×C₄₇	—	4	1	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	4	no	—
214	C₂²×C₄₇	—	4	4	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
218	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
221	C₄×C₄₇	—	2	4	no	—
222	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
225	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
227	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
228	Dic₄₇	—	4	8	no	—
229	C₂²×#131	—	47	1	no	—
230	C₂×#413	D₄₇	1	1	yes	characteristic
231	C₂×#410	—	47	1	no	—
232	C₂×#405	—	47	2	no	—
233	#1757	—	47	8	no	—
234	C₂×#344	—	47	2	no	—
235	C₂×C₄₇	—	2	2	no	—
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	2	no	—
239	C₂×C₄₇	—	4	4	no	—
240	C₂×C₄₇	#1757	1	2	yes	complemented
241	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#131	—	47	4	no	—
244	C₂×#131	—	47	4	no	—
245	C₂×#131	—	94	2	no	—
246	C₂×#131	—	94	2	no	—
247	C₂×#131	—	94	4	no	—
248	C₂²×M₁₆	—	47	2	no	—
249	C₂²×M₁₆	—	47	1	no	—
250	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
251	C₂³×C₈	—	47	1	no	—
252	C₂³×C₈	—	47	2	no	—
253	C₂×#117	—	47	2	no	—
254	#413	Dic₄₇	1	4	yes	complemented
255	#413	C₂×D₄₇	1	4	yes	—
256	C₂×#101	Dic₄₇	1	2	yes	complemented
257	C₂×#100	Dic₄₇	1	2	yes	complemented
258	#410	—	47	4	no	—
259	#410	—	47	4	no	—
260	C₂×#99	—	47	4	no	—
261	#405	—	47	8	no	—
262	#405	—	94	4	no	—
263	C₂×#97	—	94	2	no	—
264	C₂×C₄×C₈	—	94	2	no	—
265	#344	—	47	8	no	—
266	C₄₇	C₂×#1757	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	C₄×D₄₇	1	2	yes	—
272	C₂×#41	C₄×D₄₇	1	2	yes	—
273	C₂×#41	C₂×Dic₄₇	1	2	yes	—
274	C₂×#41	C₂²×D₄₇	1	2	yes	—
275	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂²×D₄	C₄×D₄₇	1	2	yes	—
277	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
278	C₂³×C₄	C₄×D₄₇	1	2	yes	—
279	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
280	#131	—	94	8	no	—
281	#131	—	94	8	no	—
282	#131	—	94	8	no	—
283	#131	—	94	8	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	47	2	no	—
288	C₂×M₁₆	—	47	8	no	—
289	C₂×M₁₆	—	47	2	no	—
290	C₂×M₁₆	—	94	4	no	—
291	C₂×M₁₆	—	94	4	no	—
292	C₂×M₁₆	—	94	2	no	—
293	C₂×M₁₆	—	94	2	no	—
294	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
295	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
296	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₂²×C₈	—	47	2	no	—
303	C₂²×C₈	—	47	4	no	—
304	C₂²×C₈	—	47	2	no	—
305	C₂²×C₈	—	47	2	no	—
306	C₂²×C₈	—	47	8	no	—
307	C₂²×C₈	—	94	4	no	—
308	C₂²×C₈	—	94	2	no	—
309	C₂²×C₈	—	94	2	no	—
310	#117	—	47	4	no	—
311	#117	—	47	4	no	—
312	#117	—	94	2	no	—
313	#117	—	94	2	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₂²⋊C₄	—	47	4	no	—
316	C₂×C₄²	—	94	2	no	—
317	#101	C₂×Dic₄₇	1	8	yes	complemented
318	#100	C₂×Dic₄₇	1	8	yes	complemented
319	#99	—	47	16	no	—
320	#97	—	94	8	no	—
321	C₄×C₈	—	94	8	no	—
322	C₂⁴	C₄×Dic₄₇	1	2	yes	—
323	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₄×Dic₄₇	1	2	yes	—
335	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
341	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
342	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
343	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	94	4	no	—
349	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
350	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
351	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
352	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₄₇	1	2	yes	—
356	C₂²×C₄	D₄×D₄₇	1	2	yes	—
357	C₂²×C₄	#10625352	1	2	yes	—
358	C₂²×C₄	#10625352	1	2	yes	—
359	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
360	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	94	16	no	—
366	M₁₆	—	94	4	no	—
367	M₁₆	—	94	4	no	—
368	M₁₆	C₂²×Dic₄₇	1	8	yes	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	47	2	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	47	4	no	—
375	C₂×C₈	—	47	4	no	—
376	C₂×C₈	—	47	1	no	—
377	C₂×C₈	—	47	1	no	—
378	C₂×C₈	—	47	2	no	—
379	C₂×C₈	—	47	2	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	47	4	no	—
382	C₂×C₈	—	47	4	no	—
383	C₂×C₈	—	47	4	no	—
384	C₂×C₈	—	94	8	no	—
385	C₂×C₈	—	94	8	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	94	2	no	—
388	C₄⋊C₄	—	94	4	no	—
389	C₄⋊C₄	—	94	4	no	—
390	C₂²⋊C₄	—	47	8	no	—
391	C₂²⋊C₄	—	94	4	no	—
392	C₄²	—	94	4	no	—
393	C₄²	—	94	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	4	no	—
398	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
399	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
400	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
401	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
402	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
403	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	4	no	—
406	D₄	—	2	8	no	—
407	D₄	—	2	8	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	94	8	no	—
417	C₂×C₄	—	188	8	no	—
418	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
419	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
423	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	#13093980	1	1	yes	characteristic
425	C₂×C₄	#13093980	1	1	yes	characteristic
426	C₂×C₄	#13093980	1	2	yes	—
427	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
428	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
429	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
430	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
431	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
432	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
433	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
436	C₂×C₄	C₂×#10625352	1	2	yes	—
437	C₈	—	2	8	no	—
438	C₈	—	47	2	no	—
439	C₈	—	47	2	no	—
440	C₈	—	47	4	no	—
441	C₈	—	94	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
452	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
453	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
454	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
455	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
456	C₄	—	2	4	no	—
457	C₄	—	188	8	no	—
458	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
459	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
460	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
461	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
462	C₄	C₂×#13093980	1	1	yes	characteristic
463	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
464	C₂	—	2	2	no	—
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	4	no	—
469	C₂	#20243191	1	2	yes	direct product factor
470	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#413	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#413	D₄₇
hypocenter	C₄₇	C₂×#1757
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#413

Complements

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

N	H ≅ G/N	type
3. C₂×#15689081	C₂	semidirect
4. #20243191	C₂	direct (N × H)
5. C₂×#15688895	C₂	semidirect
10. C₂×#13094031	C₄	semidirect
12. C₂²×#10625329	C₄	semidirect
14. C₂³×C₄₇⋊C₈	C₄	semidirect
21. #15689081	C₂²	semidirect
24. #15688895	C₂²	semidirect
27. C₄₇×#413	C₄	semidirect
29. C₂×#101×C₄₇	C₄	semidirect
30. C₂×#100×C₄₇	C₄	semidirect
40. C₂×#10625329	C₂×C₄	semidirect
49. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
84. #101×C₄₇	C₂×C₄	semidirect
85. #100×C₄₇	C₂×C₄	semidirect
240. C₂×C₄₇	#1757	semidirect
254. #413	Dic₄₇	semidirect
256. C₂×#101	Dic₄₇	semidirect
257. C₂×#100	Dic₄₇	semidirect
266. C₄₇	C₂×#1757	semidirect
317. #101	C₂×Dic₄₇	semidirect
318. #100	C₂×Dic₄₇	semidirect
469. C₂	#20243191	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×#13094031	2
C₂×#15689097	2
C₂×#15689081	2
#20243191	2
C₂×#15688895	2
C₂×C₄₇×#413	2
C₂×#1757	47

Subgroups — C2×#20243191 #26213979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243191 #26213979