Subgroups — #26220315

Order 12032.

1610 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689140	C₂	1	4	yes	maximal, complemented
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244308	C₂	1	8	yes	maximal, complemented
5	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689140	—	2	16	no	—
9	C₂×#13093951	C₂²	1	16	yes	complemented
10	C₄×#10625329	—	2	2	no	—
11	C₄×#10625329	C₂²	1	4	yes	complemented
12	C₂×#13093935	—	2	1	no	—
13	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
14	#15688993	—	2	1	no	—
15	#15688989	—	2	1	no	—
16	#15688983	—	2	2	no	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	complemented
18	C₂²×#41×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#532	—	2	1	no	—
20	C₄₇×#532	—	2	1	no	—
21	C₄₇×#532	—	2	1	no	—
22	C₄₇×#532	—	2	1	no	—
23	C₄₇×#532	C₄	1	4	yes	complemented
24	C₄₇×#532	C₂²	1	4	yes	—
25	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
26	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
27	C₂×#124×C₄₇	C₄	1	2	yes	complemented
28	C₂×#121×C₄₇	—	2	2	no	—
29	C₂×C₄×D₄×C₄₇	—	2	2	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	D₄	1	8	yes	complemented
34	C₂×#10625329	C₂³	1	4	yes	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	#13093983	—	2	8	no	—
37	C₂×C₄⋊Dic₄₇	—	2	4	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
41	#13093951	—	2	32	no	—
42	#13093935	—	2	4	no	—
43	C₄×C₄₇⋊C₈	—	2	4	no	—
44	C₄₇⋊#95	—	2	4	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	8	no	—
48	C₂×#41×C₄₇	—	2	8	no	—
49	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
50	C₂×#41×C₄₇	C₂³	1	4	yes	—
51	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₄₇	—	2	2	no	—
53	C₂²×D₄×C₄₇	—	2	2	no	—
54	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₄₇	—	2	2	no	—
56	C₂³×C₄×C₄₇	D₄	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	—	2	1	no	—
60	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
61	#127×C₄₇	—	2	1	no	—
62	#127×C₄₇	—	2	1	no	—
63	#127×C₄₇	C₂×C₄	1	4	yes	—
64	#124×C₄₇	—	2	2	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	C₂×C₄	1	8	yes	—
67	#121×C₄₇	—	2	4	no	—
68	#121×C₄₇	—	2	4	no	—
69	#121×C₄₇	—	2	4	no	—
70	#121×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	4	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	D₄	1	2	yes	—
83	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂⁴×C₄₇	—	2	2	no	—
87	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
88	#41×C₄₇	—	2	16	no	—
89	#41×C₄₇	—	2	8	no	—
90	#41×C₄₇	—	2	8	no	—
91	#41×C₄₇	—	4	8	no	—
92	#41×C₄₇	—	4	4	no	—
93	#41×C₄₇	—	4	4	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	8	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂×D₄×C₄₇	—	2	4	no	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	8	no	—
103	C₂×D₄×C₄₇	—	4	8	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	4	8	no	—
112	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₄₇	#41	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂²×Dic₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	4	no	—
129	C₂²⋊C₄×C₄₇	—	2	8	no	—
130	C₂²⋊C₄×C₄₇	—	2	8	no	—
131	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
138	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	C₂×D₄	1	2	yes	—
140	C₄²×C₄₇	C₂×D₄	1	2	yes	—
141	C₂²⋊Dic₄₇	—	4	4	no	—
142	C₄⋊Dic₄₇	—	4	8	no	—
143	C₄⋊Dic₄₇	—	4	4	no	—
144	C₄×Dic₄₇	—	2	8	no	—
145	#10625329	—	2	8	no	—
146	#10625329	—	2	4	no	—
147	#10625329	C₂×D₄	1	8	yes	complemented
148	C₂×C₄₇⋊C₈	—	2	8	no	—
149	C₂×C₄₇⋊C₈	—	2	4	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	8	no	—
153	C₂³×C₄₇	—	4	4	no	—
154	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₄₇	#124	1	2	yes	—
157	C₂³×C₄₇	#127	1	2	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	8	no	—
160	Q₈×C₄₇	—	4	4	no	—
161	D₄×C₄₇	—	2	8	no	—
162	D₄×C₄₇	—	4	8	no	—
163	D₄×C₄₇	—	4	4	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	4	8	no	—
166	D₄×C₄₇	—	4	4	no	—
167	D₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	8	no	—
177	C₂×C₄×C₄₇	—	4	8	no	—
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₄₇	#121	1	4	yes	—
187	C₂×C₄×C₄₇	#121	1	4	yes	—
188	C₂×C₄×C₄₇	#124	1	2	yes	—
189	C₂×C₄×C₄₇	#127	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
194	C₂×Dic₄₇	—	4	8	no	—
195	C₂×Dic₄₇	—	4	4	no	—
196	C₄₇⋊C₈	—	2	8	no	—
197	#21252	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	4	8	no	—
204	C₂²×C₄₇	—	4	4	no	—
205	C₂²×C₄₇	—	8	8	no	—
206	C₂²×C₄₇	#390	1	2	yes	—
207	C₂²×C₄₇	#390	1	2	yes	—
208	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	#390	1	2	yes	—
216	C₄×C₄₇	#390	1	2	yes	—
217	C₄×C₄₇	#421	1	4	yes	complemented
218	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
219	C₄×C₄₇	C₂×#121	1	2	yes	—
220	Dic₄₇	—	8	4	no	—
221	C₂×#532	D₄₇	1	1	yes	characteristic
222	C₂×#421	—	47	4	no	—
223	C₂×C₄×M₁₆	—	47	1	no	—
224	#2285	—	47	1	no	—
225	#1980	—	47	8	no	—
226	C₂×C₄₇	—	2	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	—	2	2	no	—
230	C₂×C₄₇	—	8	4	no	—
231	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#421	1	2	yes	—
233	C₂²×#41	C₂×D₄₇	1	2	yes	—
234	C₂²×M₁₆	—	47	2	no	—
235	#532	—	2	1	no	—
236	#532	—	2	1	no	—
237	#532	—	2	1	no	—
238	#532	—	2	1	no	—
239	#532	Dic₄₇	1	4	yes	complemented
240	#532	C₂×D₄₇	1	4	yes	—
241	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
242	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
243	C₂×#124	Dic₄₇	1	2	yes	complemented
244	C₂×#121	—	2	2	no	—
245	C₂×C₄×D₄	—	2	2	no	—
246	C₂×#117	—	47	2	no	—
247	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
248	#421	—	94	16	no	—
249	C₂×#104	—	47	16	no	—
250	C₄×M₁₆	—	47	4	no	—
251	C₄×M₁₆	—	94	2	no	—
252	C₂×#97	—	94	1	no	—
253	C₂×C₄×C₈	—	94	1	no	—
254	#384	—	94	1	no	—
255	#382	—	94	1	no	—
256	#380	—	94	2	no	—
257	C₄×C₄⋊C₄	—	47	4	no	—
258	C₄₇	#21252	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	8	no	—
262	C₂×#41	—	2	8	no	—
263	C₂×#41	C₂×Dic₄₇	1	4	yes	—
264	C₂×#41	C₂²×D₄₇	1	4	yes	—
265	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
271	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
272	C₂×M₁₆	—	47	8	no	—
273	C₂×M₁₆	—	47	4	no	—
274	C₂×M₁₆	—	94	4	no	—
275	C₂×M₁₆	—	94	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
280	#127	—	2	1	no	—
281	#127	—	2	1	no	—
282	#127	C₂×Dic₄₇	1	4	yes	—
283	#124	—	2	2	no	—
284	#124	—	2	2	no	—
285	#124	C₂×Dic₄₇	1	8	yes	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	C₄×D₄	—	2	4	no	—
294	#117	—	94	8	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	4	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	94	2	no	—
300	C₂×C₄²	—	47	4	no	—
301	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
302	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
303	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
307	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
310	#104	—	94	32	no	—
311	#97	—	94	4	no	—
312	C₄×C₈	—	94	4	no	—
313	#95	—	94	4	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
316	#41	—	2	16	no	—
317	#41	—	2	8	no	—
318	#41	—	2	8	no	—
319	#41	—	4	8	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	8	no	—
340	C₂²×C₄	—	94	4	no	—
341	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
342	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
344	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
345	C₂²×C₄	D₄×D₄₇	1	4	yes	—
346	C₂²×C₄	#10625352	1	4	yes	—
347	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
355	M₁₆	—	47	8	no	—
356	M₁₆	—	94	8	no	—
357	M₁₆	—	94	4	no	—
358	C₂×C₈	—	94	8	no	—
359	C₂×C₈	—	94	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	188	8	no	—
363	C₄⋊C₄	—	188	4	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₂²⋊C₄	—	188	4	no	—
367	C₄²	—	94	8	no	—
368	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
369	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
370	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
371	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
372	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
373	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
374	C₄²	C₂²×Dic₄₇	1	2	yes	—
375	C₄²	C₂²×Dic₄₇	1	2	yes	—
376	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
377	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	4	no	—
382	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
383	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂³	#13094011	1	2	yes	—
385	C₂³	#13094020	1	2	yes	—
386	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
387	Q₈	—	2	8	no	—
388	Q₈	—	4	4	no	—
389	D₄	—	2	8	no	—
390	D₄	—	4	8	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	8	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	188	8	no	—
407	C₂×C₄	—	188	4	no	—
408	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
409	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
411	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
414	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
415	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
416	C₂×C₄	#13093995	1	4	yes	—
417	C₂×C₄	#13093995	1	4	yes	—
418	C₂×C₄	#13094011	1	2	yes	—
419	C₂×C₄	#13094020	1	2	yes	—
420	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
422	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625352	1	2	yes	—
424	C₈	—	94	8	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	8	8	no	—
433	C₂²	#15689026	1	2	yes	—
434	C₂²	#15689026	1	2	yes	—
435	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
436	C₂²	C₂×#13094011	1	1	yes	characteristic
437	C₂²	C₂×#13094020	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	376	4	no	—
443	C₄	#15689026	1	2	yes	—
444	C₄	#15689026	1	2	yes	—
445	C₄	#15689140	1	4	yes	complemented
446	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
447	C₄	C₂×#13093995	1	2	yes	—
448	C₂	—	2	1	no	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	1	no	—
452	C₂	—	8	4	no	—
453	C₂	C₂×#15689026	1	1	yes	characteristic
454	C₂	C₂×#15689140	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#21252
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#15689140	C₂	semidirect
2. C₂×C₄×#10625329	C₂	semidirect
3. #20245795	C₂	semidirect
4. #20244308	C₂	semidirect
9. C₂×#13093951	C₂²	semidirect
11. C₄×#10625329	C₂²	semidirect
17. C₄×C₄⋊Dic₄₇	C₂²	semidirect
23. C₄₇×#532	C₄	semidirect
25. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
26. C₂×#127×C₄₇	C₄	semidirect
27. C₂×#124×C₄₇	C₄	semidirect
33. C₂×#10625329	D₄	semidirect
147. #10625329	C₂×D₄	semidirect
217. C₄×C₄₇	#421	semidirect
239. #532	Dic₄₇	semidirect
241. C₂×C₄⋊Q₈	Dic₄₇	semidirect
242. C₂×#127	Dic₄₇	semidirect
243. C₂×#124	Dic₄₇	semidirect
258. C₄₇	#21252	semidirect
445. C₄	#15689140	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689140	2
C₂×C₄×#10625329	2
#20245795	2
#20244308	2
C₂×C₄₇×#532	2
#21252	47