Subgroups — #26379221

Order 12032.

2586 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246562	C₂	1	4	yes	maximal, complemented
2	#20246463	C₂	1	4	yes	maximal, complemented
3	#20246237	C₂	1	4	yes	maximal, complemented
4	Q₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
5	D₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
6	#20246203	C₂	1	4	yes	maximal, complemented
7	#20246101	C₂	1	4	yes	maximal, complemented
8	#20246002	C₂	1	2	yes	maximal, complemented
9	#20245986	C₂	1	2	yes	maximal, complemented
10	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	complemented
14	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
15	C₂×#13093983	C₂²	1	2	yes	—
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
17	#15689030	C₂²	1	8	yes	complemented
18	#15689030	C₂²	1	4	yes	complemented
19	#15689026	C₂²	1	4	yes	—
20	#15689016	C₂²	1	8	yes	complemented
21	#15689016	C₂²	1	8	yes	complemented
22	#15689016	C₂²	1	8	yes	complemented
23	#15689016	C₂²	1	8	yes	complemented
24	#15689003	C₂²	1	8	yes	—
25	#15688998	C₂²	1	8	yes	complemented
26	#15688998	C₂²	1	8	yes	complemented
27	#15688998	C₂²	1	8	yes	complemented
28	#15688993	C₂²	1	2	yes	complemented
29	#15688991	C₂²	1	2	yes	complemented
30	#15688989	C₂²	1	2	yes	complemented
31	#15688989	C₂²	1	2	yes	complemented
32	#15688986	C₂²	1	2	yes	—
33	#15688983	C₂²	1	1	yes	characteristic
34	#15688983	C₂²	1	1	yes	characteristic
35	#15688983	C₂²	1	2	yes	—
36	#15688983	C₂²	1	2	yes	—
37	#15688983	C₂²	1	4	yes	—
38	#15688979	C₂²	1	4	yes	—
39	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
40	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
41	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
42	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
43	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
44	C₄×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
45	#15688969	C₂²	1	2	yes	complemented
46	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
48	C₂×#124×C₄₇	C₄	1	16	yes	complemented
49	C₂×#124×C₄₇	C₂²	1	2	yes	—
50	C₂×#124×C₄₇	C₂²	1	2	yes	—
51	C₂×#124×C₄₇	C₂²	1	2	yes	—
52	C₂×#124×C₄₇	C₂²	1	2	yes	—
53	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
54	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
55	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
56	C₂³×Dic₄₇	C₂³	1	8	yes	—
57	Q₈×Dic₄₇	—	4	8	no	—
58	D₄×Dic₄₇	—	4	8	no	—
59	#13093983	—	4	4	no	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
61	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
65	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
66	C₂×C₂²⋊Dic₄₇	—	4	8	no	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
69	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
71	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
72	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
73	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
74	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
75	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
76	C₄₇⋊#95	C₂³	1	2	yes	—
77	C₄₇⋊#95	C₂³	1	2	yes	—
78	C₄₇⋊#95	C₂³	1	4	yes	—
79	C₄₇⋊#95	C₂³	1	4	yes	—
80	C₄₇⋊#95	C₂³	1	8	yes	—
81	C₄₇⋊#95	C₂³	1	4	yes	—
82	C₄₇⋊#95	C₂³	1	8	yes	—
83	C₄₇⋊#95	C₂³	1	4	yes	—
84	C₄₇⋊#95	C₂³	1	4	yes	—
85	C₂⁵×C₄₇	C₂³	1	2	yes	—
86	C₂²×Q₈×C₄₇	—	4	4	no	—
87	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
88	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
89	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
90	C₂²×D₄×C₄₇	—	4	4	no	—
91	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
92	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
94	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
97	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
98	#124×C₄₇	C₂×C₄	1	16	yes	complemented
99	#124×C₄₇	C₂×C₄	1	16	yes	complemented
100	#124×C₄₇	C₂×C₄	1	16	yes	complemented
101	#124×C₄₇	C₂×C₄	1	16	yes	complemented
102	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
103	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
104	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₂⁴×C₄₇	—	2	4	no	—
114	C₂⁴×C₄₇	—	2	4	no	—
115	C₂⁴×C₄₇	—	4	4	no	—
116	C₂⁴×C₄₇	—	4	4	no	—
117	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
118	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
119	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₄₇	—	2	8	no	—
121	C₂×Q₈×C₄₇	—	4	4	no	—
122	C₂×Q₈×C₄₇	—	4	16	no	—
123	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
124	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₄₇	—	2	8	no	—
126	C₂×D₄×C₄₇	—	4	16	no	—
127	C₂×D₄×C₄₇	—	4	4	no	—
128	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
129	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	4	2	no	—
134	C₂²×C₄×C₄₇	—	4	4	no	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂²×Dic₄₇	—	4	8	no	—
147	C₂²×Dic₄₇	—	4	8	no	—
148	C₂²×Dic₄₇	—	4	8	no	—
149	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
150	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
151	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
152	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
153	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
154	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
155	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
156	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
157	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
158	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
159	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
160	C₂²⋊Dic₄₇	—	2	4	no	—
161	C₂²⋊Dic₄₇	—	2	8	no	—
162	C₂²⋊Dic₄₇	—	2	4	no	—
163	C₂²⋊Dic₄₇	—	4	8	no	—
164	C₂²⋊Dic₄₇	—	4	8	no	—
165	C₂²⋊Dic₄₇	—	4	8	no	—
166	C₄⋊Dic₄₇	—	2	8	no	—
167	C₄⋊Dic₄₇	—	4	2	no	—
168	C₄⋊Dic₄₇	—	4	4	no	—
169	C₄⋊Dic₄₇	—	4	2	no	—
170	C₄⋊Dic₄₇	—	4	4	no	—
171	C₄⋊Dic₄₇	—	4	8	no	—
172	C₄×Dic₄₇	—	2	8	no	—
173	C₄×Dic₄₇	—	4	4	no	—
174	C₄×Dic₄₇	—	4	8	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	4	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	—	2	8	no	—
181	C₂³×C₄₇	—	2	16	no	—
182	C₂³×C₄₇	—	4	8	no	—
183	C₂³×C₄₇	—	4	8	no	—
184	C₂³×C₄₇	—	8	8	no	—
185	C₂³×C₄₇	—	8	8	no	—
186	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
187	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
188	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
189	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
190	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
191	Q₈×C₄₇	—	2	16	no	—
192	Q₈×C₄₇	—	4	8	no	—
193	D₄×C₄₇	—	2	16	no	—
194	D₄×C₄₇	—	4	8	no	—
195	C₂×C₄×C₄₇	—	2	8	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	8	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	8	no	—
205	C₂×C₄×C₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	—	4	8	no	—
207	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
212	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
213	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
215	C₂×Dic₄₇	—	2	4	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	2	8	no	—
218	C₂×Dic₄₇	—	2	8	no	—
219	C₂×Dic₄₇	—	2	4	no	—
220	C₂×Dic₄₇	—	2	4	no	—
221	C₂×Dic₄₇	—	2	4	no	—
222	C₂×Dic₄₇	—	2	8	no	—
223	C₂×Dic₄₇	—	2	4	no	—
224	C₂×Dic₄₇	—	8	16	no	—
225	#34377	—	47	1	no	maximal, Sylow
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	2	2	no	—
228	C₂²×C₄₇	—	2	4	no	—
229	C₂²×C₄₇	—	2	4	no	—
230	C₂²×C₄₇	—	2	8	no	—
231	C₂²×C₄₇	—	2	8	no	—
232	C₂²×C₄₇	—	2	8	no	—
233	C₂²×C₄₇	—	4	8	no	—
234	C₂²×C₄₇	—	4	8	no	—
235	C₂²×C₄₇	—	8	16	no	—
236	C₂²×C₄₇	#520	1	4	yes	—
237	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
238	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
239	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
241	C₂²×C₄₇	#585	1	2	yes	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	2	8	no	—
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	#518	1	4	yes	—
249	Dic₄₇	—	4	8	no	—
250	Dic₄₇	—	4	4	no	—
251	Dic₄₇	—	4	4	no	—
252	C₂²×#124	D₄₇	1	1	yes	characteristic
253	#2379	—	47	4	no	—
254	#2367	—	47	4	no	—
255	#2342	—	47	4	no	—
256	Q₈×C₂²⋊C₄	—	47	2	no	—
257	D₄×C₂²⋊C₄	—	47	2	no	—
258	#2337	—	47	4	no	—
259	#2326	—	47	4	no	—
260	#2315	—	47	2	no	—
261	#2312	—	47	2	no	—
262	#2285	—	47	1	no	—
263	#2283	—	47	1	no	—
264	C₂×C₄₇	—	2	4	no	—
265	C₂×C₄₇	—	4	8	no	—
266	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
267	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
268	C₂×C₄₇	#3428	1	1	yes	characteristic
269	C₂×C₄₇	#3558	1	2	yes	—
270	C₂×C₄₇	#3561	1	2	yes	—
271	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
272	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
273	C₂×#124	Dic₄₇	1	16	yes	complemented
274	C₂×#124	C₂×D₄₇	1	2	yes	—
275	C₂×#124	C₂×D₄₇	1	2	yes	—
276	C₂×#124	C₂×D₄₇	1	2	yes	—
277	C₂×#124	C₂×D₄₇	1	2	yes	—
278	C₂×C₄×Q₈	—	47	4	no	—
279	C₂×C₄×D₄	—	47	4	no	—
280	C₂×#117	—	47	2	no	—
281	C₂²×C₂²⋊C₄	—	47	4	no	—
282	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
284	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
285	#391	—	47	4	no	—
286	#391	—	47	8	no	—
287	#390	—	47	4	no	—
288	#388	—	47	8	no	—
289	#388	—	47	8	no	—
290	#388	—	47	8	no	—
291	#388	—	47	8	no	—
292	#386	—	47	8	no	—
293	#385	—	47	8	no	—
294	#385	—	47	8	no	—
295	#385	—	47	8	no	—
296	#384	—	47	2	no	—
297	#383	—	47	2	no	—
298	#382	—	47	2	no	—
299	#382	—	47	2	no	—
300	#381	—	47	2	no	—
301	#380	—	47	1	no	—
302	#380	—	47	2	no	—
303	#380	—	47	1	no	—
304	#380	—	47	4	no	—
305	#380	—	47	2	no	—
306	#379	—	47	4	no	—
307	C₄×C₄⋊C₄	—	47	2	no	—
308	C₄×C₄⋊C₄	—	47	2	no	—
309	C₄×C₄⋊C₄	—	47	2	no	—
310	C₄×C₂²⋊C₄	—	47	4	no	—
311	C₄×C₂²⋊C₄	—	47	2	no	—
312	C₄×C₂²⋊C₄	—	47	8	no	—
313	#376	—	47	2	no	—
314	C₄₇	#34377	1	1	yes	characteristic, complemented, Sylow
315	C₂⁵	C₂²×D₄₇	1	2	yes	—
316	C₂²×Q₈	—	4	4	no	—
317	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	complemented
318	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
319	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
320	C₂²×D₄	—	4	4	no	—
321	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
322	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
323	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
324	C₂³×C₄	—	47	8	no	—
325	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
326	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
327	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
328	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
329	#124	C₂×Dic₄₇	1	16	yes	complemented
330	#124	C₂×Dic₄₇	1	16	yes	complemented
331	#124	C₂×Dic₄₇	1	16	yes	complemented
332	#124	C₂×Dic₄₇	1	16	yes	complemented
333	C₄×Q₈	—	188	8	no	—
334	C₄×D₄	—	188	8	no	—
335	#117	—	188	4	no	—
336	C₂×C₄⋊C₄	—	47	4	no	—
337	C₂×C₄⋊C₄	—	47	4	no	—
338	C₂×C₄⋊C₄	—	47	8	no	—
339	C₂×C₄⋊C₄	—	47	2	no	—
340	C₂×C₄⋊C₄	—	47	2	no	—
341	C₂×C₄⋊C₄	—	47	4	no	—
342	C₂×C₂²⋊C₄	—	47	2	no	—
343	C₂×C₂²⋊C₄	—	47	4	no	—
344	C₂×C₂²⋊C₄	—	47	2	no	—
345	C₂×C₂²⋊C₄	—	47	8	no	—
346	C₂×C₂²⋊C₄	—	47	8	no	—
347	C₂×C₂²⋊C₄	—	47	8	no	—
348	C₂×C₂²⋊C₄	—	188	8	no	—
349	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
350	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
351	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
355	C₂×C₄²	—	47	4	no	—
356	C₂×C₄²	—	47	4	no	—
357	C₂×C₄²	—	47	8	no	—
358	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
359	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
360	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
361	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
363	#95	—	47	2	no	—
364	#95	—	47	2	no	—
365	#95	—	47	4	no	—
366	#95	—	47	4	no	—
367	#95	—	47	8	no	—
368	#95	—	47	4	no	—
369	#95	—	47	8	no	—
370	#95	—	47	4	no	—
371	#95	—	47	4	no	—
372	C₂⁴	—	2	4	no	—
373	C₂⁴	—	2	4	no	—
374	C₂⁴	—	4	4	no	—
375	C₂⁴	—	4	4	no	—
376	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
377	C₂⁴	C₂³×D₄₇	1	4	yes	—
378	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×Q₈	—	4	16	no	—
382	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
383	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂×D₄	—	4	4	no	—
387	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
388	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	47	4	no	—
395	C₂²×C₄	—	47	4	no	—
396	C₂²×C₄	—	47	8	no	—
397	C₂²×C₄	—	188	8	no	—
398	C₂²×C₄	—	188	8	no	—
399	C₂²×C₄	—	188	8	no	—
400	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
401	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
402	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
403	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
404	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
407	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	C₄⋊C₄	—	94	8	no	—
412	C₄⋊C₄	—	188	2	no	—
413	C₄⋊C₄	—	188	4	no	—
414	C₄⋊C₄	—	188	2	no	—
415	C₄⋊C₄	—	188	4	no	—
416	C₄⋊C₄	—	188	8	no	—
417	C₂²⋊C₄	—	94	4	no	—
418	C₂²⋊C₄	—	94	8	no	—
419	C₂²⋊C₄	—	94	4	no	—
420	C₂²⋊C₄	—	188	8	no	—
421	C₂²⋊C₄	—	188	8	no	—
422	C₂²⋊C₄	—	188	8	no	—
423	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
424	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
425	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
426	C₂²⋊C₄	C₂²×Dic₄₇	1	16	yes	—
427	C₄²	—	94	8	no	—
428	C₄²	—	188	4	no	—
429	C₄²	—	188	8	no	—
430	C₄²	C₂²×Dic₄₇	1	4	yes	—
431	C₄²	C₂²×Dic₄₇	1	4	yes	—
432	C₄²	C₂²×Dic₄₇	1	4	yes	—
433	C₄²	C₂²×Dic₄₇	1	4	yes	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	16	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	4	8	no	—
443	C₂³	—	8	8	no	—
444	C₂³	—	8	8	no	—
445	C₂³	C₂³×Dic₄₇	1	8	yes	—
446	C₂³	C₂³×Dic₄₇	1	2	yes	—
447	C₂³	#13094070	1	2	yes	—
448	C₂³	#13094071	1	2	yes	—
449	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
450	Q₈	—	2	16	no	—
451	Q₈	—	4	8	no	—
452	D₄	—	2	16	no	—
453	D₄	—	4	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	94	4	no	—
467	C₂×C₄	—	94	4	no	—
468	C₂×C₄	—	94	8	no	—
469	C₂×C₄	—	94	8	no	—
470	C₂×C₄	—	94	4	no	—
471	C₂×C₄	—	94	4	no	—
472	C₂×C₄	—	94	4	no	—
473	C₂×C₄	—	94	8	no	—
474	C₂×C₄	—	94	4	no	—
475	C₂×C₄	—	376	16	no	—
476	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
477	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
478	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
479	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
480	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
481	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
482	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
483	C₂×C₄	#13094069	1	4	yes	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	8	no	—
489	C₂²	—	2	8	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	4	8	no	—
493	C₂²	—	8	16	no	—
494	C₂²	#15689606	1	4	yes	—
495	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
496	C₂²	C₂×#13094069	1	2	yes	—
497	C₂²	C₂×#13094070	1	1	yes	characteristic
498	C₂²	C₂×#13094071	1	1	yes	characteristic
499	C₂²	#15689959	1	2	yes	—
500	C₄	—	2	2	no	—
501	C₄	—	2	8	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	188	4	no	—
507	C₄	—	188	8	no	—
508	C₄	—	188	4	no	—
509	C₄	#15689598	1	4	yes	—
510	C₂	—	2	4	no	—
511	C₂	—	4	8	no	—
512	C₂	C₂×#15689598	1	1	yes	characteristic
513	C₂	C₂×#15689606	1	1	yes	characteristic
514	C₂	#20256591	1	1	yes	characteristic
515	C₂	#20257907	1	2	yes	—
516	C₂	#20257960	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂²×#124×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂²×#124	D₄₇
hypocenter	C₄₇	#34377
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. #20246562	C₂	semidirect
2. #20246463	C₂	semidirect
3. #20246237	C₂	semidirect
4. Q₈×C₂²⋊Dic₄₇	C₂	semidirect
6. #20246203	C₂	semidirect
7. #20246101	C₂	semidirect
8. #20246002	C₂	semidirect
9. #20245986	C₂	semidirect
10. #20245795	C₂	semidirect
11. #20245786	C₂	semidirect
13. C₂×Q₈×Dic₄₇	C₂²	semidirect
17. #15689030	C₂²	semidirect
18. #15689030	C₂²	semidirect
20. #15689016	C₂²	semidirect
21. #15689016	C₂²	semidirect
22. #15689016	C₂²	semidirect
23. #15689016	C₂²	semidirect
25. #15688998	C₂²	semidirect
26. #15688998	C₂²	semidirect
27. #15688998	C₂²	semidirect
28. #15688993	C₂²	semidirect
29. #15688991	C₂²	semidirect
30. #15688989	C₂²	semidirect
31. #15688989	C₂²	semidirect
39. C₄×C₄⋊Dic₄₇	C₂²	semidirect
40. C₄×C₄⋊Dic₄₇	C₂²	semidirect
41. C₄×C₄⋊Dic₄₇	C₂²	semidirect
42. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
45. #15688969	C₂²	semidirect
48. C₂×#124×C₄₇	C₄	semidirect
87. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
98. #124×C₄₇	C₂×C₄	semidirect
99. #124×C₄₇	C₂×C₄	semidirect
100. #124×C₄₇	C₂×C₄	semidirect
101. #124×C₄₇	C₂×C₄	semidirect
102. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
103. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
108. C₂×C₄²×C₄₇	C₂×C₄	semidirect
273. C₂×#124	Dic₄₇	semidirect
314. C₄₇	#34377	semidirect
317. C₂²×Q₈	C₂×Dic₄₇	semidirect
329. #124	C₂×Dic₄₇	semidirect
330. #124	C₂×Dic₄₇	semidirect
331. #124	C₂×Dic₄₇	semidirect
332. #124	C₂×Dic₄₇	semidirect
349. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
350. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
358. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246562	2
#20246463	2
#20246237	2
Q₈×C₂²⋊Dic₄₇	2
D₄×C₂²⋊Dic₄₇	2
#20246203	2
#20246101	2
#20246002	2
#20245986	2
#20245795	2
#20245786	2
C₂²×#124×C₄₇	2
#34377	47