Subgroups — #26232192

Order 12032.

1336 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252248	C₂	1	2	yes	maximal, complemented
2	#20251852	C₂	1	1	yes	maximal, characteristic, complemented
3	#20251849	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244287	C₂	1	2	yes	maximal, complemented
5	#20243884	C₂	1	2	yes	maximal, complemented
6	#20243877	C₂	1	2	yes	maximal, complemented
7	#20243434	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243363	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243358	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#577	C₂	1	1	yes	maximal, characteristic
12	#15689601	C₂²	1	2	yes	complemented
13	#15689598	C₂²	1	2	yes	—
14	#15689224	—	2	4	no	—
15	SD₁₆×Dic₄₇	—	2	4	no	—
16	#15689161	C₂²	1	2	yes	complemented
17	#15689140	C₂²	1	2	yes	—
18	#15689140	C₂²	1	2	yes	complemented
19	#15689132	C₂²	1	2	yes	complemented
20	#15689128	C₂²	1	2	yes	—
21	#15689107	C₂²	1	1	yes	characteristic
22	#15689097	—	2	4	no	—
23	#15689097	C₂²	1	2	yes	—
24	#15689097	C₂²	1	1	yes	characteristic
25	#15689097	C₂²	1	1	yes	characteristic
26	#15689097	C₂²	1	1	yes	characteristic
27	#15689097	C₂²	1	2	yes	complemented
28	C₂×#13093939	—	2	4	no	—
29	#15689078	C₂²	1	2	yes	complemented
30	#15688894	C₂²	1	2	yes	complemented
31	#15688880	C₂²	1	2	yes	complemented
32	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×H(5,𝔽₂)×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#577	—	2	4	no	—
35	C₄₇×#577	—	2	4	no	—
36	C₂×#137×C₄₇	C₄	1	2	yes	complemented
37	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	2	yes	complemented
39	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#135×C₄₇	C₄	1	2	yes	complemented
41	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
43	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625329	C₂³	1	2	yes	—
46	Q₈×Dic₄₇	—	2	4	no	—
47	Q₈×Dic₄₇	—	4	2	no	—
48	D₄×Dic₄₇	—	2	4	no	—
49	D₄×Dic₄₇	—	4	2	no	—
50	#13093983	—	2	4	no	—
51	#13093983	C₂³	1	2	yes	—
52	#13093983	C₂³	1	2	yes	—
53	#13093983	C₂³	1	2	yes	—
54	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
55	#13093958	—	2	2	no	—
56	#13093956	—	2	2	no	—
57	#13093951	—	4	2	no	—
58	#13093951	—	4	2	no	—
59	#13093948	—	2	4	no	—
60	#13093945	—	2	4	no	—
61	#13093943	—	2	1	no	—
62	#13093941	—	2	1	no	—
63	#13093939	—	2	2	no	—
64	#13093939	—	2	2	no	—
65	#13093939	—	2	4	no	—
66	#13093939	—	2	4	no	—
67	#13093939	D₄	1	4	yes	—
68	#13093934	—	2	2	no	—
69	C₈×Dic₄₇	—	2	2	no	—
70	2₋¹⁺⁴×C₄₇	—	2	4	no	—
71	2₋¹⁺⁴×C₄₇	—	4	2	no	—
72	H(5,𝔽₂)×C₄₇	—	2	4	no	—
73	H(5,𝔽₂)×C₄₇	—	4	2	no	—
74	C₂×#41×C₄₇	—	2	1	no	—
75	C₂×#41×C₄₇	—	2	2	no	—
76	C₂×#41×C₄₇	—	2	1	no	—
77	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
79	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₄₇	—	2	1	no	—
83	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
84	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₄₇	—	2	2	no	—
86	C₂²×D₄×C₄₇	—	2	1	no	—
87	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
88	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
89	#137×C₄₇	—	2	4	no	—
90	#137×C₄₇	—	2	8	no	—
91	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
92	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
93	#135×C₄₇	—	2	4	no	—
94	#135×C₄₇	—	2	4	no	—
95	#135×C₄₇	—	2	2	no	—
96	#135×C₄₇	—	2	2	no	—
97	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
98	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×SD₁₆×C₄₇	—	2	4	no	—
100	C₂×SD₁₆×C₄₇	—	2	4	no	—
101	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
103	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
104	C₂×SD₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
106	C₂×SD₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂×SD₁₆×C₄₇	D₄	1	4	yes	—
108	C₂×SD₁₆×C₄₇	D₄	1	4	yes	—
109	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
110	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
111	#131×C₄₇	—	2	2	no	—
112	#131×C₄₇	—	2	2	no	—
113	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
114	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂⁴×C₄₇	—	2	1	no	—
118	C₂⁴×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	4	no	—
122	#41×C₄₇	—	2	4	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	4	2	no	—
128	#41×C₄₇	—	4	2	no	—
129	#41×C₄₇	—	4	8	no	—
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	4	no	—
132	C₂×Q₈×C₄₇	—	2	2	no	—
133	C₂×Q₈×C₄₇	—	2	1	no	—
134	C₂×Q₈×C₄₇	—	2	2	no	—
135	C₂×Q₈×C₄₇	—	2	4	no	—
136	C₂×Q₈×C₄₇	—	4	2	no	—
137	C₂×Q₈×C₄₇	—	4	4	no	—
138	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
142	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
143	C₂×D₄×C₄₇	—	2	4	no	—
144	C₂×D₄×C₄₇	—	2	2	no	—
145	C₂×D₄×C₄₇	—	2	2	no	—
146	C₂×D₄×C₄₇	—	2	1	no	—
147	C₂×D₄×C₄₇	—	2	1	no	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	1	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	4	2	no	—
152	C₂×D₄×C₄₇	—	4	4	no	—
153	C₂×D₄×C₄₇	—	4	8	no	—
154	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
159	C₂×D₄×C₄₇	#41	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	—	2	2	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	1	no	—
166	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²×Dic₄₇	—	4	4	no	—
169	Q₁₆×C₄₇	—	2	4	no	—
170	Q₁₆×C₄₇	—	2	2	no	—
171	SD₁₆×C₄₇	—	2	4	no	—
172	SD₁₆×C₄₇	—	2	4	no	—
173	SD₁₆×C₄₇	—	2	1	no	—
174	SD₁₆×C₄₇	—	2	1	no	—
175	SD₁₆×C₄₇	—	2	1	no	—
176	SD₁₆×C₄₇	—	2	1	no	—
177	SD₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
178	SD₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
179	SD₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
180	D₈×C₄₇	—	2	4	no	—
181	D₈×C₄₇	—	2	2	no	—
182	M₁₆×C₄₇	—	2	2	no	—
183	M₁₆×C₄₇	—	2	4	no	—
184	C₂×C₈×C₄₇	—	2	2	no	—
185	C₂×C₈×C₄₇	—	2	2	no	—
186	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
187	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	—	4	4	no	—
194	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
195	C₄⋊Dic₄₇	—	2	2	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	C₄⋊Dic₄₇	—	2	2	no	—
198	C₄⋊Dic₄₇	—	4	4	no	—
199	C₄×Dic₄₇	—	2	2	no	—
200	C₄×Dic₄₇	—	2	2	no	—
201	C₄×Dic₄₇	—	2	2	no	—
202	C₄×Dic₄₇	—	4	4	no	—
203	#10625329	—	2	2	no	—
204	#10625329	—	2	2	no	—
205	C₂×C₄₇⋊C₈	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	4	no	—
208	C₂³×C₄₇	—	2	1	no	—
209	C₂³×C₄₇	—	2	1	no	—
210	C₂³×C₄₇	—	4	4	no	—
211	C₂³×C₄₇	—	16	1	no	—
212	C₂³×C₄₇	—	16	2	no	—
213	C₂³×C₄₇	C₄×D₄	1	2	yes	—
214	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₄₇	—	2	2	no	—
216	Q₈×C₄₇	—	2	4	no	—
217	Q₈×C₄₇	—	2	2	no	—
218	Q₈×C₄₇	—	2	1	no	—
219	Q₈×C₄₇	—	2	1	no	—
220	Q₈×C₄₇	—	2	1	no	—
221	Q₈×C₄₇	—	2	1	no	—
222	Q₈×C₄₇	—	4	4	no	—
223	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
224	D₄×C₄₇	—	2	4	no	—
225	D₄×C₄₇	—	2	1	no	—
226	D₄×C₄₇	—	2	1	no	—
227	D₄×C₄₇	—	2	2	no	—
228	D₄×C₄₇	—	2	1	no	—
229	D₄×C₄₇	—	2	1	no	—
230	D₄×C₄₇	—	2	4	no	—
231	D₄×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	4	4	no	—
233	D₄×C₄₇	—	4	4	no	—
234	D₄×C₄₇	—	4	4	no	—
235	D₄×C₄₇	—	4	2	no	—
236	D₄×C₄₇	—	4	2	no	—
237	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	4	4	no	—
245	C₂×C₄×C₄₇	—	4	4	no	—
246	C₂×C₄×C₄₇	—	4	4	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
250	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
254	C₂×Dic₄₇	—	2	4	no	—
255	C₂×Dic₄₇	—	4	2	no	—
256	C₂×Dic₄₇	—	4	2	no	—
257	C₂×Dic₄₇	—	16	4	no	—
258	C₈×C₄₇	—	2	2	no	—
259	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
262	C₄₇⋊C₈	—	4	2	no	—
263	#22456	—	47	1	no	maximal, Sylow
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	4	no	—
266	C₂²×C₄₇	—	4	1	no	—
267	C₂²×C₄₇	—	4	2	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	—	4	1	no	—
270	C₂²×C₄₇	—	8	4	no	—
271	C₂²×C₄₇	—	8	2	no	—
272	C₂²×C₄₇	—	8	1	no	—
273	C₂²×C₄₇	—	8	1	no	—
274	C₂²×C₄₇	—	16	4	no	—
275	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₄₇	D₄²	1	2	yes	—
277	C₄×C₄₇	—	2	4	no	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	4	1	no	—
280	C₄×C₄₇	—	4	1	no	—
281	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
282	C₄×C₄₇	#518	1	1	yes	characteristic
283	C₄×C₄₇	#546	1	2	yes	—
284	Dic₄₇	—	4	4	no	—
285	Dic₄₇	—	8	2	no	—
286	Dic₄₇	—	8	2	no	—
287	C₂×#577	D₄₇	1	1	yes	characteristic
288	#2949	—	47	2	no	—
289	#2884	—	47	1	no	—
290	#2883	—	47	1	no	—
291	#1976	—	47	2	no	—
292	#1905	—	47	2	no	—
293	#1904	—	47	2	no	—
294	#1812	—	47	1	no	—
295	#1796	—	47	1	no	—
296	#1795	—	47	1	no	—
297	#1757	—	47	1	no	—
298	C₂×C₄₇	—	2	2	no	—
299	C₂×C₄₇	—	2	1	no	—
300	C₂×C₄₇	—	4	2	no	—
301	C₂×C₄₇	—	4	4	no	—
302	C₂×C₄₇	—	8	1	no	—
303	C₂×C₄₇	—	8	1	no	—
304	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic
306	C₂×H(5,𝔽₂)	C₂×D₄₇	1	1	yes	characteristic
307	#577	—	2	4	no	—
308	#577	—	2	4	no	—
309	C₂×#137	Dic₄₇	1	2	yes	complemented
310	C₂×#137	C₂×D₄₇	1	1	yes	characteristic
311	C₂×AGL(1,ℤ/8)	Dic₄₇	1	2	yes	complemented
312	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	1	yes	characteristic
313	C₂×#135	Dic₄₇	1	2	yes	complemented
314	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
315	C₂²×SD₁₆	Dic₄₇	1	2	yes	complemented
316	C₂²×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
317	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
318	#519	—	47	2	no	—
319	#518	—	47	2	no	—
320	#440	—	94	4	no	—
321	C₄×SD₁₆	—	94	4	no	—
322	#427	—	47	2	no	—
323	#421	—	47	2	no	—
324	#421	—	47	2	no	—
325	#419	—	47	2	no	—
326	#418	—	47	2	no	—
327	#413	—	47	1	no	—
328	#410	—	47	1	no	—
329	#410	—	47	1	no	—
330	#410	—	47	1	no	—
331	#410	—	47	2	no	—
332	#410	—	47	2	no	—
333	#410	—	94	4	no	—
334	C₂×#99	—	94	4	no	—
335	#405	—	47	2	no	—
336	#344	—	47	2	no	—
337	H(3,ℤ/4)	—	47	2	no	—
338	C₄₇	#22456	1	1	yes	characteristic, complemented, Sylow
339	2₋¹⁺⁴	—	2	4	no	—
340	2₋¹⁺⁴	—	4	2	no	—
341	H(5,𝔽₂)	—	2	4	no	—
342	H(5,𝔽₂)	—	4	2	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	C₂×Dic₄₇	1	2	yes	—
347	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
348	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
349	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
350	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
351	C₂²×Q₈	—	2	1	no	—
352	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	complemented
353	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
357	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
358	#137	—	2	4	no	—
359	#137	—	2	8	no	—
360	AGL(1,ℤ/8)	—	2	4	no	—
361	AGL(1,ℤ/8)	—	2	8	no	—
362	#135	—	2	4	no	—
363	#135	—	2	4	no	—
364	#135	—	2	2	no	—
365	#135	—	2	2	no	—
366	C₂×Q₁₆	C₂×Dic₄₇	1	2	yes	complemented
367	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
368	C₂×SD₁₆	—	2	4	no	—
369	C₂×SD₁₆	—	2	4	no	—
370	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
371	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
372	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
373	C₂×SD₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
374	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	complemented
375	C₂×SD₁₆	C₂×Dic₄₇	1	1	yes	characteristic, complemented
376	C₂×SD₁₆	C₂²⋊D₄₇	1	4	yes	—
377	C₂×SD₁₆	C₂²⋊D₄₇	1	4	yes	—
378	C₂×D₈	C₂×Dic₄₇	1	2	yes	—
379	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
380	#131	—	2	2	no	—
381	#131	—	2	2	no	—
382	C₂×M₁₆	—	47	2	no	—
383	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	complemented
384	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
385	C₂²×C₈	C₂×Dic₄₇	1	2	yes	complemented
386	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
387	C₄×Q₈	—	94	4	no	—
388	C₄×Q₈	—	188	2	no	—
389	C₄×D₄	—	94	4	no	—
390	C₄×D₄	—	188	2	no	—
391	#117	—	47	2	no	—
392	#117	—	47	2	no	—
393	#117	—	47	2	no	—
394	#117	—	94	4	no	—
395	C₂×C₂²⋊C₄	—	94	4	no	—
396	#107	—	94	2	no	—
397	#106	—	94	2	no	—
398	#104	—	188	2	no	—
399	#104	—	188	2	no	—
400	#103	—	94	4	no	—
401	#102	—	94	4	no	—
402	#101	—	94	1	no	—
403	#100	—	94	1	no	—
404	#99	—	47	4	no	—
405	#99	—	94	4	no	—
406	#99	—	94	4	no	—
407	#99	—	94	2	no	—
408	#99	—	94	2	no	—
409	#97	—	94	2	no	—
410	C₄×C₈	—	94	2	no	—
411	C₂⁴	—	2	1	no	—
412	C₂⁴	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	4	2	no	—
422	#41	—	4	2	no	—
423	#41	—	4	8	no	—
424	#41	—	4	4	no	—
425	#41	—	4	4	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	#10625352	1	1	yes	characteristic
433	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
434	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
435	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
436	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	8	no	—
448	C₂×D₄	D₄×D₄₇	1	2	yes	—
449	C₂×D₄	#10625352	1	1	yes	characteristic
450	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
451	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
452	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
453	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	188	4	no	—
461	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
462	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
463	Q₁₆	—	2	4	no	—
464	Q₁₆	—	2	2	no	—
465	SD₁₆	—	2	4	no	—
466	SD₁₆	—	2	4	no	—
467	SD₁₆	—	2	1	no	—
468	SD₁₆	—	2	1	no	—
469	SD₁₆	—	2	1	no	—
470	SD₁₆	—	2	1	no	—
471	SD₁₆	C₂²⋊Dic₄₇	1	4	yes	—
472	SD₁₆	C₂²⋊Dic₄₇	1	4	yes	—
473	SD₁₆	C₂²⋊Dic₄₇	1	8	yes	—
474	D₈	—	2	4	no	—
475	D₈	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	4	no	—
478	M₁₆	—	94	2	no	—
479	M₁₆	—	94	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	94	2	no	—
483	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
484	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
485	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
486	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
487	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
488	C₄⋊C₄	—	94	2	no	—
489	C₄⋊C₄	—	94	2	no	—
490	C₄⋊C₄	—	94	2	no	—
491	C₄⋊C₄	—	188	4	no	—
492	C₂²⋊C₄	—	47	4	no	—
493	C₂²⋊C₄	—	94	2	no	—
494	C₂²⋊C₄	—	94	2	no	—
495	C₂²⋊C₄	—	188	4	no	—
496	C₄²	—	94	2	no	—
497	C₄²	—	94	2	no	—
498	C₄²	—	94	2	no	—
499	C₄²	—	188	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	4	4	no	—
505	C₂³	—	16	1	no	—
506	C₂³	—	16	2	no	—
507	C₂³	D₄×Dic₄₇	1	2	yes	—
508	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	4	4	no	—
517	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
518	D₄	—	2	4	no	—
519	D₄	—	2	4	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	94	4	no	—
544	C₂×C₄	—	188	2	no	—
545	C₂×C₄	—	188	2	no	—
546	C₂×C₄	—	752	4	no	—
547	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
548	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
550	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
551	C₂×C₄	#13094069	1	2	yes	—
552	C₈	—	2	2	no	—
553	C₈	—	188	2	no	—
554	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
555	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
556	C₈	C₂×C₂²⋊Dic₄₇	1	2	yes	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	16	4	no	—
568	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
569	C₂²	D₄×C₂²⋊D₄₇	1	2	yes	—
570	C₄	—	2	4	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	376	2	no	—
575	C₄	—	376	2	no	—
576	C₄	—	188	4	no	—
577	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
578	C₄	#15689598	1	1	yes	characteristic
579	C₄	#15689767	1	2	yes	—
580	C₂	—	2	2	no	—
581	C₂	—	2	1	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	4	no	—
584	C₂	—	8	1	no	—
585	C₂	—	8	1	no	—
586	C₂	D₄×C₂²⋊Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#577	C₂
socle	C₂×C₄₇	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#577	D₄₇
hypocenter	C₄₇	#22456
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#577

Complements

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

N	H ≅ G/N	type
1. #20252248	C₂	semidirect
2. #20251852	C₂	semidirect
3. #20251849	C₂	semidirect
4. #20244287	C₂	semidirect
5. #20243884	C₂	semidirect
6. #20243877	C₂	semidirect
7. #20243434	C₂	semidirect
8. #20243363	C₂	semidirect
9. #20243358	C₂	semidirect
10. #20243188	C₂	semidirect
12. #15689601	C₂²	semidirect
16. #15689161	C₂²	semidirect
18. #15689140	C₂²	semidirect
19. #15689132	C₂²	semidirect
27. #15689097	C₂²	semidirect
29. #15689078	C₂²	semidirect
30. #15688894	C₂²	semidirect
31. #15688880	C₂²	semidirect
36. C₂×#137×C₄₇	C₄	semidirect
38. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
40. C₂×#135×C₄₇	C₄	semidirect
42. C₂²×SD₁₆×C₄₇	C₄	semidirect
78. C₂×#41×C₄₇	C₂×C₄	semidirect
83. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
97. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
98. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
104. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
105. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
106. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
110. C₂×D₈×C₄₇	C₂×C₄	semidirect
113. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
115. C₂²×C₈×C₄₇	C₂×C₄	semidirect
309. C₂×#137	Dic₄₇	semidirect
311. C₂×AGL(1,ℤ/8)	Dic₄₇	semidirect
313. C₂×#135	Dic₄₇	semidirect
315. C₂²×SD₁₆	Dic₄₇	semidirect
338. C₄₇	#22456	semidirect
347. C₂×#41	C₂×Dic₄₇	semidirect
352. C₂²×Q₈	C₂×Dic₄₇	semidirect
366. C₂×Q₁₆	C₂×Dic₄₇	semidirect
367. C₂×Q₁₆	C₂×Dic₄₇	semidirect
373. C₂×SD₁₆	C₂×Dic₄₇	semidirect
374. C₂×SD₁₆	C₂×Dic₄₇	semidirect
375. C₂×SD₁₆	C₂×Dic₄₇	semidirect
379. C₂×D₈	C₂×Dic₄₇	semidirect
383. C₂×M₁₆	C₂×Dic₄₇	semidirect
385. C₂²×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252248	2
#20251852	2
#20251849	2
#20244287	2
#20243884	2
#20243877	2
#20243434	2
#20243363	2
#20243358	2
#20243188	2
C₂×C₄₇×#577	2
#22456	47