Subgroups — #26220028

Order 12032.

1658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689097	C₂	1	4	yes	maximal, complemented
2	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244225	C₂	1	8	yes	maximal, complemented
5	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689097	—	2	16	no	—
9	C₂×#13093939	C₂²	1	16	yes	—
10	#15688993	—	2	1	no	—
11	#15688989	—	2	1	no	—
12	#15688983	C₂²	1	4	yes	—
13	C₄×C₄⋊Dic₄₇	—	2	2	no	—
14	C₄×C₄⋊Dic₄₇	—	2	2	no	—
15	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
16	#15688969	—	2	1	no	—
17	C₄²×Dic₄₇	—	2	1	no	—
18	C₂²×#41×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#532	—	2	1	no	—
20	C₄₇×#532	—	2	1	no	—
21	C₄₇×#532	—	2	2	no	—
22	C₄₇×#532	—	2	2	no	—
23	C₄₇×#532	—	2	1	no	—
24	C₄₇×#532	—	2	1	no	—
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	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	complemented
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	#13093983	—	2	4	no	—
32	#13093983	—	2	8	no	—
33	#13093983	D₄	1	8	yes	complemented
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
38	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	4	no	—
41	C₂×C₄×Dic₄₇	—	2	2	no	—
42	#13093939	—	2	32	no	—
43	C₄₇⋊#95	—	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	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	—	2	8	no	—
50	C₂×#41×C₄₇	—	2	8	no	—
51	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	—	2	2	no	—
60	C₄⋊Q₈×C₄₇	—	2	1	no	—
61	#127×C₄₇	—	2	1	no	—
62	#127×C₄₇	—	2	2	no	—
63	#127×C₄₇	—	2	1	no	—
64	#124×C₄₇	—	2	2	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	4	no	—
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	C₂×C₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
77	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
86	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
88	#41×C₄₇	—	4	8	no	—
89	#41×C₄₇	—	4	8	no	—
90	#41×C₄₇	—	4	4	no	—
91	#41×C₄₇	—	4	4	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	2	no	—
96	C₂×Q₈×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	4	no	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	8	no	—
100	C₂×D₄×C₄₇	—	2	8	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	8	no	—
106	C₂×D₄×C₄₇	—	4	8	no	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	16	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
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	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₇	#41	1	4	yes	—
126	C₂²×Dic₄₇	—	2	4	no	—
127	C₂²×Dic₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	4	no	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	2	8	no	—
131	C₂²⋊C₄×C₄₇	—	2	8	no	—
132	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
141	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²⋊Dic₄₇	—	2	4	no	—
143	C₂²⋊Dic₄₇	—	2	8	no	—
144	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
145	C₄⋊Dic₄₇	—	2	8	no	—
146	C₄⋊Dic₄₇	—	4	8	no	—
147	C₄⋊Dic₄₇	—	4	4	no	—
148	C₄×Dic₄₇	—	2	8	no	—
149	C₄×Dic₄₇	—	4	8	no	—
150	C₄×Dic₄₇	—	4	4	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	8	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	8	no	—
155	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂³×C₄₇	C₂×#41	1	2	yes	—
160	Q₈×C₄₇	—	4	4	no	—
161	Q₈×C₄₇	—	4	4	no	—
162	D₄×C₄₇	—	4	8	no	—
163	D₄×C₄₇	—	4	8	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	4	4	no	—
166	D₄×C₄₇	—	4	4	no	—
167	D₄×C₄₇	—	4	4	no	—
168	D₄×C₄₇	—	4	8	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	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	8	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	8	no	—
178	C₂×C₄×C₄₇	—	4	8	no	—
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	2	yes	—
182	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₄₇	#121	1	4	yes	—
190	C₂×C₄×C₄₇	#121	1	4	yes	—
191	C₂×C₄×C₄₇	#124	1	2	yes	—
192	C₂×C₄×C₄₇	#124	1	2	yes	—
193	C₂×C₄×C₄₇	#127	1	2	yes	—
194	C₂×C₄×C₄₇	#127	1	2	yes	—
195	C₂×Dic₄₇	—	2	8	no	—
196	C₂×Dic₄₇	—	4	8	no	—
197	C₂×Dic₄₇	—	4	8	no	—
198	C₂×Dic₄₇	—	4	4	no	—
199	#21212	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	8	no	—
206	C₂²×C₄₇	—	4	4	no	—
207	C₂²×C₄₇	—	8	8	no	—
208	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
210	C₂²×C₄₇	C₂×#121	1	2	yes	—
211	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	#390	1	2	yes	—
218	C₄×C₄₇	#390	1	2	yes	—
219	C₄×C₄₇	#390	1	2	yes	—
220	C₄×C₄₇	#390	1	2	yes	—
221	C₄×C₄₇	#410	1	4	yes	complemented
222	Dic₄₇	—	4	8	no	—
223	Dic₄₇	—	8	4	no	—
224	C₂×#532	D₄₇	1	1	yes	characteristic
225	C₂×#410	—	47	4	no	—
226	#2285	—	47	1	no	—
227	C₄×#117	—	47	1	no	—
228	#1964	—	47	8	no	—
229	C₂×C₄₇	—	2	2	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	8	4	no	—
234	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#410	1	2	yes	—
236	C₂²×#41	C₂×D₄₇	1	2	yes	—
237	#532	—	2	1	no	—
238	#532	—	2	1	no	—
239	#532	—	2	2	no	—
240	#532	—	2	2	no	—
241	#532	—	2	1	no	—
242	#532	—	2	1	no	—
243	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
244	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
245	C₂×#124	Dic₄₇	1	2	yes	complemented
246	C₂×#121	C₂×D₄₇	1	4	yes	—
247	C₂×C₄×D₄	Dic₄₇	1	4	yes	complemented
248	C₂×#117	—	47	2	no	—
249	C₂×#117	—	47	2	no	—
250	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
251	#410	—	94	16	no	—
252	C₂×#99	—	47	16	no	—
253	#384	—	94	1	no	—
254	#382	—	94	1	no	—
255	#380	—	47	4	no	—
256	C₄×C₄⋊C₄	—	94	2	no	—
257	C₄×C₄⋊C₄	—	94	2	no	—
258	C₄×C₂²⋊C₄	—	47	4	no	—
259	#376	—	94	1	no	—
260	C₄³	—	94	1	no	—
261	C₄₇	#21212	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	2	8	no	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	—	2	2	no	—
268	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
269	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
270	C₂²×D₄	C₂×Dic₄₇	1	4	yes	—
271	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
272	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
273	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
274	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	2	no	—
280	#127	—	2	1	no	—
281	#124	—	2	2	no	—
282	#124	—	2	2	no	—
283	#124	—	2	4	no	—
284	#121	—	2	4	no	—
285	#121	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	2	4	no	—
292	#117	—	47	8	no	—
293	#117	—	94	4	no	—
294	#117	—	94	8	no	—
295	C₂×C₄⋊C₄	—	94	2	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	—	94	4	no	—
298	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
299	C₂×C₂²⋊C₄	—	47	4	no	—
300	C₂×C₂²⋊C₄	—	47	4	no	—
301	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
302	C₂×C₄²	—	94	2	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	—	94	4	no	—
305	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
306	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
307	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
310	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
311	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
312	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
313	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
314	#99	—	94	32	no	—
315	#95	—	94	4	no	—
316	#95	—	94	4	no	—
317	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
318	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
319	#41	—	4	8	no	—
320	#41	—	4	8	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	8	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	4	8	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	16	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	94	4	no	—
343	C₂²×C₄	—	94	4	no	—
344	C₂²×C₄	D₄×D₄₇	1	4	yes	—
345	C₂²×C₄	#10625352	1	4	yes	—
346	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
347	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
348	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
349	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
355	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	94	8	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	—	47	8	no	—
367	C₂²⋊C₄	—	94	4	no	—
368	C₂²⋊C₄	—	94	8	no	—
369	C₄²	—	94	8	no	—
370	C₄²	—	188	8	no	—
371	C₄²	—	188	4	no	—
372	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
373	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
374	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
375	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
376	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
377	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
378	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
379	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
380	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
381	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	8	no	—
386	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
387	C₂³	C₂×D₄×D₄₇	1	2	yes	—
388	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂³	C₂×#10625352	1	2	yes	—
391	Q₈	—	4	4	no	—
392	Q₈	—	4	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	4	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	8	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	94	8	no	—
411	C₂×C₄	—	188	8	no	—
412	C₂×C₄	—	188	4	no	—
413	C₂×C₄	—	188	8	no	—
414	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
415	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
416	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
417	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
420	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
421	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
422	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
423	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
424	C₂×C₄	#13093995	1	4	yes	—
425	C₂×C₄	#13093995	1	4	yes	—
426	C₂×C₄	#13094011	1	2	yes	—
427	C₂×C₄	#13094011	1	2	yes	—
428	C₂×C₄	#13094020	1	2	yes	—
429	C₂×C₄	#13094020	1	2	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	8	no	—
437	C₂²	—	8	8	no	—
438	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
439	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
440	C₂²	C₂×#13093995	1	2	yes	—
441	C₂²	C₂×#13094011	1	1	yes	characteristic
442	C₂²	C₂×#13094020	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	376	4	no	—
448	C₄	—	188	8	no	—
449	C₄	#15689026	1	2	yes	—
450	C₄	#15689026	1	2	yes	—
451	C₄	#15689026	1	2	yes	—
452	C₄	#15689026	1	2	yes	—
453	C₄	#15689097	1	4	yes	complemented
454	C₂	—	2	1	no	—
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	2	1	no	—
458	C₂	—	8	4	no	—
459	C₂	C₂×#15689026	1	1	yes	characteristic
460	C₂	C₂×#15689097	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂⁴	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#21212
LCS	G ▷ C₂³×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×#15689097	C₂	semidirect
2. #20245795	C₂	semidirect
3. C₄×#13093983	C₂	semidirect
4. #20244225	C₂	semidirect
25. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
26. C₂×#127×C₄₇	C₄	semidirect
27. C₂×#124×C₄₇	C₄	semidirect
29. C₂×C₄×D₄×C₄₇	C₄	semidirect
33. #13093983	D₄	semidirect
221. C₄×C₄₇	#410	semidirect
243. C₂×C₄⋊Q₈	Dic₄₇	semidirect
244. C₂×#127	Dic₄₇	semidirect
245. C₂×#124	Dic₄₇	semidirect
247. C₂×C₄×D₄	Dic₄₇	semidirect
261. C₄₇	#21212	semidirect
453. C₄	#15689097	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689097	2
#20245795	2
C₄×#13093983	2
#20244225	2
C₂×C₄₇×#532	2
#21212	47