Subgroups — C₂×#20243595 #26217063

Order 12032.

1470 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093960	C₂	1	2	yes	maximal, complemented
3	C₂×#15689087	C₂	1	1	yes	maximal, characteristic
4	#20243595	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688888	C₂	1	2	yes	maximal, complemented
6	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	—	2	8	no	—
8	C₂²×#10625329	—	2	1	no	—
9	C₂²×#10625329	—	2	2	no	—
10	C₂²×#10625329	C₂²	1	4	yes	—
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂³×C₄₇⋊C₈	—	2	1	no	—
15	C₂×#13093960	—	2	8	no	—
16	C₂×#13093960	C₂²	1	8	yes	complemented
17	#15689087	—	2	2	no	—
18	#15689087	C₂²	1	4	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
21	#15688888	C₂²	1	8	yes	complemented
22	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₇	C₄	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₄	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₇	C₄	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
28	C₂×#10625329	—	2	16	no	—
29	C₂×#10625329	—	2	8	no	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	2	4	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	16	no	—
34	C₂×#10625329	—	2	1	no	—
35	C₂×#10625329	—	2	1	no	—
36	C₂×#10625329	—	2	4	no	—
37	C₂×#10625329	—	2	4	no	—
38	C₂×#10625329	D₄	1	8	yes	—
39	C₂×#10625329	C₂³	1	2	yes	—
40	C₂×#10625329	C₂³	1	2	yes	—
41	C₂×#10625329	C₂³	1	4	yes	—
42	C₂²×C₄₇⋊C₈	—	2	8	no	—
43	C₂²×C₄₇⋊C₈	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	1	no	—
46	C₂²×C₄₇⋊C₈	—	2	1	no	—
47	#13093960	—	2	16	no	—
48	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
49	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
50	C₂⁵×C₄₇	Q₈	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	4	no	—
53	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	D₄	1	2	yes	—
59	C₂³×C₄×C₄₇	Q₈	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	—	2	4	no	—
64	C₂²×C₈×C₄₇	—	2	4	no	—
65	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
66	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
68	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
69	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	4	2	no	—
73	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
75	C₂⁴×C₄₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
77	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	8	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₄₇	—	2	8	no	—
112	C₂×C₈×C₄₇	—	2	8	no	—
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
116	#10625329	—	2	16	no	—
117	#10625329	—	2	8	no	—
118	#10625329	—	2	4	no	—
119	#10625329	—	2	4	no	—
120	#10625329	—	2	4	no	—
121	#10625329	—	4	2	no	—
122	#10625329	—	4	2	no	—
123	#10625329	C₂×D₄	1	8	yes	—
124	C₂×C₄₇⋊C₈	—	2	16	no	—
125	C₂×C₄₇⋊C₈	—	2	8	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	4	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	16	no	—
145	C₂³×C₄₇	#108	1	4	yes	complemented
146	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
149	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
151	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
171	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
172	C₂×C₄×C₄₇	#120	1	2	yes	—
173	C₂×C₄×C₄₇	#120	1	2	yes	—
174	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₄₇	#123	1	2	yes	—
176	C₂×C₄×C₄₇	#123	1	2	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
181	C₈×C₄₇	—	2	8	no	—
182	C₄₇⋊C₈	—	2	8	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	C₂×#1855	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	8	no	—
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	8	no	—
198	C₂²×C₄₇	—	4	8	no	—
199	C₂²×C₄₇	—	4	4	no	—
200	C₂²×C₄₇	#385	1	2	yes	—
201	C₂²×C₄₇	#385	1	2	yes	—
202	C₂²×C₄₇	C₂×#108	1	2	yes	—
203	C₂²×C₄₇	C₂×#108	1	4	yes	complemented
204	C₂²×C₄₇	#430	1	2	yes	—
205	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	#385	1	2	yes	—
210	C₄×C₄₇	#385	1	2	yes	—
211	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
212	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
214	C₂³×M₁₆	—	47	1	no	—
215	C₂²×#108	—	47	2	no	—
216	C₂×#407	—	47	1	no	—
217	C₂²×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
218	#1855	—	47	8	no	—
219	C₂×#341	—	47	2	no	—
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	—	2	4	no	—
223	C₂×C₄₇	—	4	2	no	—
224	C₂×C₄₇	#1855	1	4	yes	complemented
225	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
226	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
228	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
229	C₂²×M₁₆	—	47	2	no	—
230	C₂²×M₁₆	—	47	1	no	—
231	C₂²×M₁₆	—	47	1	no	—
232	C₂²×M₁₆	—	47	4	no	—
233	C₂²×M₁₆	—	94	8	no	—
234	C₂²×M₁₆	—	94	2	no	—
235	C₂²×M₁₆	—	94	1	no	—
236	C₂³×C₈	—	94	1	no	—
237	C₂³×C₈	C₂×D₄₇	1	2	yes	—
238	C₂×#108	—	47	8	no	—
239	C₂×#108	—	94	8	no	—
240	#407	—	47	4	no	—
241	#407	—	94	2	no	—
242	C₂×C₂²⋊C₈	—	94	1	no	—
243	C₂×C₂²⋊C₈	—	94	1	no	—
244	C₂×C₂²⋊C₈	Dic₄₇	1	2	yes	—
245	C₂×C₂²⋊C₈	Dic₄₇	1	4	yes	—
246	C₂×C₂²⋊C₈	Dic₄₇	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂×D₄₇	1	4	yes	—
248	#341	—	47	8	no	—
249	C₄₇	C₂×#1855	1	1	yes	characteristic, complemented, Sylow
250	C₂⁵	Dic₉₄	1	1	yes	characteristic
251	C₂³×C₄	—	2	4	no	—
252	C₂³×C₄	—	2	4	no	—
253	C₂³×C₄	Dic₉₄	1	1	yes	characteristic
254	C₂³×C₄	Dic₉₄	1	2	yes	—
255	C₂³×C₄	D₁₈₈	1	2	yes	—
256	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
257	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
258	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
259	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
260	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
261	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
262	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
263	C₂×M₁₆	—	47	8	no	—
264	C₂×M₁₆	—	47	4	no	—
265	C₂×M₁₆	—	47	2	no	—
266	C₂×M₁₆	—	47	2	no	—
267	C₂×M₁₆	—	94	16	no	—
268	C₂×M₁₆	—	94	16	no	—
269	C₂×M₁₆	—	94	8	no	—
270	C₂×M₁₆	—	94	4	no	—
271	C₂×M₁₆	—	94	2	no	—
272	C₂×M₁₆	—	94	4	no	—
273	C₂×M₁₆	—	94	1	no	—
274	C₂×M₁₆	—	94	1	no	—
275	C₂×M₁₆	—	94	4	no	—
276	C₂×M₁₆	—	94	4	no	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	—	94	8	no	—
280	C₂²×C₈	—	94	4	no	—
281	C₂²×C₈	—	94	2	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₂²×C₈	—	94	1	no	—
284	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
285	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
286	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
287	#108	—	94	16	no	—
288	C₂²⋊C₈	—	94	4	no	—
289	C₂²⋊C₈	—	94	4	no	—
290	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
291	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	4	2	no	—
295	C₂⁴	C₄⋊Dic₄₇	1	1	yes	characteristic
296	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
297	C₂⁴	C₄⋊Dic₄₇	1	1	yes	characteristic
298	C₂⁴	C₂×Dic₉₄	1	2	yes	—
299	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
314	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
317	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
318	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
319	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
320	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
321	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
323	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
324	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
326	C₂²×C₄	D₄×D₄₇	1	4	yes	—
327	C₂²×C₄	#10625352	1	4	yes	—
328	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
329	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
330	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	M₁₆	—	47	8	no	—
334	M₁₆	—	94	16	no	—
335	M₁₆	—	94	8	no	—
336	M₁₆	—	94	4	no	—
337	M₁₆	—	94	4	no	—
338	M₁₆	—	94	4	no	—
339	M₁₆	—	188	2	no	—
340	M₁₆	—	188	2	no	—
341	C₂×C₈	—	2	8	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	94	16	no	—
346	C₂×C₈	—	94	8	no	—
347	C₂×C₈	—	94	4	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	188	2	no	—
351	C₂×C₈	—	188	2	no	—
352	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	16	no	—
367	C₂³	#13093960	1	4	yes	complemented
368	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
369	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
370	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
371	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
372	C₂³	#13094001	1	4	yes	—
373	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
389	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
390	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
393	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
394	C₂×C₄	#13093994	1	2	yes	—
395	C₂×C₄	#13093994	1	2	yes	—
396	C₂×C₄	#13094001	1	4	yes	—
397	C₂×C₄	#13094008	1	2	yes	—
398	C₂×C₄	#13094008	1	2	yes	—
399	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
401	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625352	1	2	yes	—
403	C₈	—	2	8	no	—
404	C₈	—	94	8	no	—
405	C₈	—	188	2	no	—
406	C₈	—	188	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	8	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	4	no	—
421	C₂²	#15688998	1	2	yes	—
422	C₂²	#15688998	1	2	yes	—
423	C₂²	C₂×#13093960	1	2	yes	—
424	C₂²	C₂×#13093960	1	4	yes	complemented
425	C₂²	#15689172	1	2	yes	—
426	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
427	C₂²	C₂×#13094001	1	2	yes	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	#15688998	1	2	yes	—
431	C₄	#15688998	1	2	yes	—
432	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
433	C₄	C₂×#13093994	1	1	yes	characteristic
434	C₄	C₂×#13094008	1	1	yes	characteristic
435	C₂	—	2	2	no	—
436	C₂	—	2	2	no	—
437	C₂	—	2	4	no	—
438	C₂	—	4	2	no	—
439	C₂	#20243595	1	4	yes	direct product factor
440	C₂	C₂×#15688998	1	1	yes	characteristic
441	C₂	C₂²×#13093960	1	1	yes	characteristic
442	C₂	C₂×#15689172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₄⋊C₄
prime radical	C₂⁵×C₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	C₂×#1855
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂⁴×C₄ ◁ C₂²×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093960	C₂	semidirect
4. #20243595	C₂	direct (N × H)
5. C₂×#15688888	C₂	semidirect
16. C₂×#13093960	C₂²	semidirect
21. #15688888	C₂²	semidirect
145. C₂³×C₄₇	#108	semidirect
203. C₂²×C₄₇	C₂×#108	semidirect
224. C₂×C₄₇	#1855	semidirect
249. C₄₇	C₂×#1855	semidirect
367. C₂³	#13093960	semidirect
424. C₂²	C₂×#13093960	semidirect
439. C₂	#20243595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625329	2
C₂²×#13093960	2
C₂×#15689087	2
#20243595	2
C₂×#15688888	2
C₂²×C₂²⋊C₈×C₄₇	2
C₂×#1855	47

Subgroups — C2×#20243595 #26217063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243595 #26217063