Subgroups — #26123282

Order 12032.

970 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251951	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689129	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689129	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13093940	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243099	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#13093983	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689151	—	2	2	no	—
13	#15689149	—	2	2	no	—
14	#15689146	—	2	2	no	—
15	#15689129	—	2	2	no	—
16	#15689129	—	2	2	no	—
17	#15689129	—	2	2	no	—
18	#15689129	—	2	2	no	—
19	C₂×#13093946	—	2	2	no	—
20	C₂×#13093946	C₄	1	4	yes	complemented
21	C₂×#13093940	—	2	2	no	—
22	C₂×#13093940	—	2	2	no	—
23	C₂×#13093940	—	2	2	no	—
24	#15688894	—	2	2	no	—
25	#15688884	—	2	2	no	—
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#338	—	2	2	no	—
30	C₂⁴×D₄₇	—	2	1	no	—
31	C₂²×D₁₈₈	—	2	1	no	—
32	C₂²×D₁₈₈	—	2	1	no	—
33	C₂²×D₁₈₈	—	2	1	no	—
34	C₂²×D₁₈₈	—	2	1	no	—
35	C₂²×D₁₈₈	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂²×D₁₈₈	—	2	1	no	—
38	C₂²×D₁₈₈	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
43	C₂²×D₁₈₈	D₄	1	2	yes	—
44	C₂²×D₁₈₈	Q₈	1	2	yes	—
45	C₂×#10625329	—	2	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	D₄	1	2	yes	—
51	C₂²×C₄₇⋊C₈	—	2	1	no	—
52	#13093983	—	2	1	no	—
53	#13093983	—	2	1	no	—
54	#13093983	—	2	1	no	—
55	#13093983	—	2	1	no	—
56	#13093983	—	2	1	no	—
57	#13093983	D₄	1	2	yes	—
58	#13093983	D₄	1	2	yes	—
59	#13093983	D₄	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
63	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	Dic₄₇⋊C₈	—	2	8	no	—
67	#13093946	—	2	8	no	—
68	#13093946	—	2	8	no	—
69	#13093940	—	2	8	no	—
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₇	—	2	1	no	—
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂×M₁₆×C₄₇	—	2	1	no	—
74	C₂×M₁₆×C₄₇	—	2	1	no	—
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	C₂×M₁₆×C₄₇	—	2	1	no	—
78	C₂×M₁₆×C₄₇	—	2	1	no	—
79	C₂×M₁₆×C₄₇	—	2	1	no	—
80	C₂×M₁₆×C₄₇	—	2	1	no	—
81	C₂×M₁₆×C₄₇	—	2	1	no	—
82	C₂×M₁₆×C₄₇	—	2	1	no	—
83	C₂×M₁₆×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	—	2	1	no	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
89	C₂²×C₈×C₄₇	—	2	1	no	—
90	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²×C₈×C₄₇	D₄	1	2	yes	—
92	C₂⁴×C₄₇	#41	1	1	yes	characteristic
93	C₂³×D₄₇	—	2	2	no	—
94	C₂³×D₄₇	—	2	2	no	—
95	C₂³×D₄₇	—	2	2	no	—
96	C₂³×D₄₇	—	4	1	no	—
97	C₂³×D₄₇	—	4	1	no	—
98	C₂³×D₄₇	—	4	1	no	—
99	C₂³×D₄₇	—	4	1	no	—
100	C₂³×D₄₇	—	8	4	no	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	4	1	no	—
117	C₂×D₁₈₈	—	2	2	no	—
118	C₂×D₁₈₈	—	2	2	no	—
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	—	2	2	no	—
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	2	2	no	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	—	2	2	no	—
131	C₂×D₁₈₈	—	2	2	no	—
132	C₂×D₁₈₈	—	4	1	no	—
133	C₂×D₁₈₈	—	4	1	no	—
134	C₂×D₁₈₈	—	4	1	no	—
135	C₂×D₁₈₈	—	4	1	no	—
136	C₂×D₁₈₈	—	4	1	no	—
137	C₂×D₁₈₈	—	4	1	no	—
138	C₂×D₁₈₈	—	4	1	no	—
139	C₂×D₁₈₈	—	4	1	no	—
140	C₂×D₁₈₈	—	4	1	no	—
141	C₂×D₁₈₈	—	4	1	no	—
142	C₂×D₁₈₈	—	4	1	no	—
143	C₂×D₁₈₈	—	4	1	no	—
144	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
145	M₁₆×C₄₇	—	2	2	no	—
146	M₁₆×C₄₇	—	2	2	no	—
147	M₁₆×C₄₇	—	4	1	no	—
148	M₁₆×C₄₇	—	4	1	no	—
149	M₁₆×C₄₇	—	4	1	no	—
150	M₁₆×C₄₇	—	4	1	no	—
151	M₁₆×C₄₇	—	4	1	no	—
152	M₁₆×C₄₇	—	4	1	no	—
153	M₁₆×C₄₇	—	4	1	no	—
154	M₁₆×C₄₇	—	4	1	no	—
155	M₁₆×C₄₇	—	4	1	no	—
156	M₁₆×C₄₇	—	4	1	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	2	no	—
162	C₂×C₈×C₄₇	—	2	2	no	—
163	C₂×C₈×C₄₇	—	2	2	no	—
164	C₂×C₈×C₄₇	—	4	1	no	—
165	C₂×C₈×C₄₇	—	4	1	no	—
166	C₂²⋊Dic₄₇	—	2	2	no	—
167	C₂²⋊Dic₄₇	—	2	2	no	—
168	C₂²⋊Dic₄₇	—	2	2	no	—
169	C₂²⋊Dic₄₇	—	4	1	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	2	2	no	—
172	C₄⋊Dic₄₇	—	4	1	no	—
173	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
174	C₄×Dic₄₇	—	2	2	no	—
175	C₄×Dic₄₇	—	2	2	no	—
176	C₄×Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	4	1	no	—
178	#10625329	—	2	2	no	—
179	#10625329	—	2	2	no	—
180	#10625329	—	4	1	no	—
181	#10625329	—	4	1	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	—	4	1	no	—
184	C₂×C₄₇⋊C₈	—	4	1	no	—
185	C₂³×C₄₇	—	4	2	no	—
186	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₄₇	#121	1	1	yes	characteristic
188	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂³×C₄₇	#123	1	1	yes	characteristic
190	C₂³×C₄₇	#123	1	1	yes	characteristic
191	C₂³×C₄₇	#123	1	1	yes	characteristic
192	C₂³×C₄₇	#126	1	1	yes	characteristic
193	C₂²×D₄₇	—	2	4	no	—
194	C₂²×D₄₇	—	4	2	no	—
195	C₂²×D₄₇	—	4	2	no	—
196	C₂²×D₄₇	—	4	2	no	—
197	C₂²×D₄₇	—	4	2	no	—
198	C₂²×D₄₇	—	4	2	no	—
199	C₂²×D₄₇	—	4	2	no	—
200	C₂²×D₄₇	—	8	4	no	—
201	C₂²×D₄₇	—	8	4	no	—
202	C₂²×D₄₇	—	8	4	no	—
203	C₂²×D₄₇	—	8	4	no	—
204	C₂²×D₄₇	—	8	4	no	—
205	C₂²×D₄₇	—	8	4	no	—
206	C₂²×D₄₇	—	8	4	no	—
207	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
216	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
217	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
219	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
235	C₂×Dic₄₇	—	2	4	no	—
236	C₂×Dic₄₇	—	4	2	no	—
237	C₂×Dic₄₇	—	8	2	no	—
238	C₂×Dic₄₇	—	8	2	no	—
239	D₁₈₈	—	2	4	no	—
240	D₁₈₈	—	2	4	no	—
241	D₁₈₈	—	4	2	no	—
242	D₁₈₈	—	4	2	no	—
243	D₁₈₈	—	4	2	no	—
244	D₁₈₈	—	4	2	no	—
245	D₁₈₈	—	4	2	no	—
246	D₁₈₈	—	4	2	no	—
247	C₈×C₄₇	—	4	2	no	—
248	C₈×C₄₇	—	4	2	no	—
249	C₈×C₄₇	—	4	2	no	—
250	C₄₇⋊C₈	—	4	2	no	—
251	#11058	—	47	1	no	maximal, Sylow
252	C₂²×C₄₇	—	2	2	no	—
253	C₂²×C₄₇	—	2	2	no	—
254	C₂²×C₄₇	—	2	2	no	—
255	C₂²×C₄₇	—	4	1	no	—
256	C₂²×C₄₇	—	4	1	no	—
257	C₂²×C₄₇	—	4	1	no	—
258	C₂²×C₄₇	—	4	1	no	—
259	C₂²×C₄₇	#385	1	1	yes	characteristic
260	C₂²×C₄₇	#386	1	1	yes	characteristic
261	C₂²×C₄₇	#388	1	1	yes	characteristic
262	C₂²×C₄₇	#394	1	1	yes	characteristic
263	C₂²×C₄₇	#396	1	1	yes	characteristic
264	C₂²×C₄₇	#397	1	1	yes	characteristic
265	C₂²×C₄₇	#399	1	1	yes	characteristic
266	C₂×D₄₇	—	4	4	no	—
267	C₂×D₄₇	—	8	4	no	—
268	C₂×D₄₇	—	8	4	no	—
269	C₂×D₄₇	—	8	4	no	—
270	C₂×D₄₇	—	8	4	no	—
271	C₂×D₄₇	—	8	4	no	—
272	C₂×D₄₇	—	8	4	no	—
273	C₂×D₄₇	—	8	4	no	—
274	C₄×C₄₇	#380	1	1	yes	characteristic
275	C₄×C₄₇	#385	1	1	yes	characteristic
276	C₄×C₄₇	#388	1	1	yes	characteristic
277	C₄×C₄₇	#390	1	1	yes	characteristic
278	C₄×C₄₇	#392	1	1	yes	characteristic
279	C₄×C₄₇	#393	1	1	yes	characteristic
280	C₄×C₄₇	#394	1	1	yes	characteristic
281	C₄×C₄₇	#396	1	1	yes	characteristic
282	Dic₄₇	—	4	4	no	—
283	Dic₄₇	—	8	2	no	—
284	#2905	—	47	1	no	—
285	C₂×#418	—	47	1	no	—
286	C₂×#418	—	47	1	no	—
287	C₂²×#100	—	47	1	no	—
288	C₂×#344	—	47	1	no	—
289	#1733	—	47	1	no	—
290	C₂×#338	D₄₇	1	1	yes	characteristic, complemented
291	C₂×C₄₇	—	2	1	no	—
292	C₂×C₄₇	—	2	1	no	—
293	C₂×C₄₇	—	2	1	no	—
294	C₂×C₄₇	—	2	1	no	—
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	2	1	no	—
297	C₂×C₄₇	#1439	1	1	yes	characteristic
298	C₂×C₄₇	#1903	1	2	yes	—
299	D₄₇	—	8	4	no	—
300	C₂³×D₄	—	47	1	no	—
301	C₂²×M₁₆	—	47	1	no	—
302	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
303	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
304	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
305	C₂×#117	—	47	1	no	—
306	C₂×#117	—	47	1	no	—
307	#424	—	94	2	no	—
308	#424	—	94	2	no	—
309	#423	—	94	2	no	—
310	#418	—	94	2	no	—
311	#418	—	94	2	no	—
312	#418	—	94	2	no	—
313	#418	—	94	2	no	—
314	C₂×#102	—	47	4	no	—
315	C₂×#102	—	94	2	no	—
316	C₂×#100	—	94	2	no	—
317	C₂×#100	—	94	2	no	—
318	C₂×#100	—	94	2	no	—
319	#344	—	94	2	no	—
320	#339	—	94	2	no	—
321	#338	—	2	2	no	—
322	C₄₇	#11058	1	1	yes	characteristic, complemented, Sylow
323	C₂⁵	—	94	1	no	—
324	C₂²×D₄	—	47	2	no	—
325	C₂²×D₄	—	47	2	no	—
326	C₂²×D₄	—	47	2	no	—
327	C₂²×D₄	—	94	1	no	—
328	C₂²×D₄	—	94	1	no	—
329	C₂²×D₄	—	94	1	no	—
330	C₂²×D₄	—	94	1	no	—
331	C₂²×D₄	—	94	1	no	—
332	C₂²×D₄	—	94	1	no	—
333	C₂²×D₄	—	94	1	no	—
334	C₂²×D₄	—	94	1	no	—
335	C₂²×D₄	—	94	1	no	—
336	C₂²×D₄	—	94	1	no	—
337	C₂²×D₄	—	94	1	no	—
338	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	47	2	no	—
357	C₂×M₁₆	—	94	1	no	—
358	C₂×M₁₆	—	94	1	no	—
359	C₂×M₁₆	—	94	1	no	—
360	C₂×M₁₆	—	94	1	no	—
361	C₂×M₁₆	—	94	1	no	—
362	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	94	1	no	—
365	C₂²×C₈	C₄×D₄₇	1	2	yes	—
366	C₂²×C₈	D₁₈₈	1	2	yes	—
367	#117	—	47	2	no	—
368	#117	—	47	2	no	—
369	#117	—	47	2	no	—
370	#117	—	94	1	no	—
371	#117	—	94	1	no	—
372	#117	—	94	1	no	—
373	#117	—	94	1	no	—
374	#117	—	94	1	no	—
375	C₂×C₄⋊C₄	—	47	2	no	—
376	C₂×C₄⋊C₄	—	94	1	no	—
377	C₂×C₂²⋊C₄	—	94	1	no	—
378	C₂×C₂²⋊C₄	—	94	1	no	—
379	C₂×C₄²	—	94	1	no	—
380	C₂×C₄²	—	94	1	no	—
381	C₄⋊C₈	—	94	8	no	—
382	#102	—	94	8	no	—
383	#102	—	94	8	no	—
384	#100	—	94	8	no	—
385	C₂⁴	—	94	2	no	—
386	C₂⁴	—	94	2	no	—
387	C₂⁴	—	94	2	no	—
388	C₂⁴	—	376	4	no	—
389	C₂⁴	—	188	1	no	—
390	C₂⁴	—	188	1	no	—
391	C₂⁴	—	188	1	no	—
392	C₂⁴	—	188	1	no	—
393	C₂⁴	#10625354	1	1	yes	characteristic
394	C₂×D₄	—	47	4	no	—
395	C₂×D₄	—	94	2	no	—
396	C₂×D₄	—	94	2	no	—
397	C₂×D₄	—	94	2	no	—
398	C₂×D₄	—	94	2	no	—
399	C₂×D₄	—	94	2	no	—
400	C₂×D₄	—	94	2	no	—
401	C₂×D₄	—	94	2	no	—
402	C₂×D₄	—	94	2	no	—
403	C₂×D₄	—	94	2	no	—
404	C₂×D₄	—	94	2	no	—
405	C₂×D₄	—	94	2	no	—
406	C₂×D₄	—	94	2	no	—
407	C₂×D₄	—	94	2	no	—
408	C₂×D₄	—	94	2	no	—
409	C₂×D₄	—	94	2	no	—
410	C₂×D₄	—	188	1	no	—
411	C₂×D₄	—	188	1	no	—
412	C₂×D₄	—	188	1	no	—
413	C₂×D₄	—	188	1	no	—
414	C₂×D₄	—	188	1	no	—
415	C₂×D₄	—	188	1	no	—
416	C₂×D₄	—	188	1	no	—
417	C₂×D₄	—	188	1	no	—
418	C₂×D₄	—	188	1	no	—
419	C₂×D₄	—	188	1	no	—
420	C₂×D₄	—	188	1	no	—
421	C₂×D₄	—	188	1	no	—
422	C₂²×C₄	—	94	2	no	—
423	C₂²×C₄	—	188	1	no	—
424	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
426	C₂²×C₄	#10625350	1	1	yes	characteristic
427	C₂²×C₄	#10625350	1	1	yes	characteristic
428	C₂²×C₄	#10625350	1	1	yes	characteristic
429	C₂²×C₄	#10625350	1	1	yes	characteristic
430	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
431	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
432	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
433	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
434	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
435	C₂²×C₄	#10625352	1	1	yes	characteristic
436	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	4	1	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	—	4	1	no	—
443	M₁₆	—	4	1	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	M₁₆	—	4	1	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	4	1	no	—
449	M₁₆	—	4	1	no	—
450	M₁₆	—	94	2	no	—
451	M₁₆	—	94	2	no	—
452	M₁₆	—	188	1	no	—
453	M₁₆	—	188	1	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	94	2	no	—
464	C₂×C₈	—	188	1	no	—
465	C₂×C₈	—	188	1	no	—
466	C₄⋊C₄	—	47	4	no	—
467	C₄⋊C₄	—	94	2	no	—
468	C₄⋊C₄	—	94	2	no	—
469	C₄⋊C₄	—	188	1	no	—
470	C₂²⋊C₄	—	94	2	no	—
471	C₂²⋊C₄	—	94	2	no	—
472	C₂²⋊C₄	—	94	2	no	—
473	C₂²⋊C₄	—	188	1	no	—
474	C₄²	—	94	2	no	—
475	C₄²	—	94	2	no	—
476	C₄²	—	94	2	no	—
477	C₄²	—	188	1	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	94	4	no	—
480	C₂³	—	376	4	no	—
481	C₂³	—	376	4	no	—
482	C₂³	—	376	4	no	—
483	C₂³	—	376	4	no	—
484	C₂³	—	376	4	no	—
485	C₂³	—	376	4	no	—
486	C₂³	—	376	4	no	—
487	C₂³	—	188	2	no	—
488	C₂³	—	188	2	no	—
489	C₂³	—	188	2	no	—
490	C₂³	—	188	2	no	—
491	C₂³	—	188	2	no	—
492	C₂³	—	188	2	no	—
493	C₂³	#13093986	1	1	yes	characteristic
494	C₂³	#13093999	1	1	yes	characteristic
495	C₂³	#13094000	1	1	yes	characteristic
496	C₂³	#13094009	1	1	yes	characteristic
497	C₂³	#13094009	1	1	yes	characteristic
498	C₂³	#13094009	1	1	yes	characteristic
499	C₂³	#13094019	1	1	yes	characteristic
500	D₄	—	94	4	no	—
501	D₄	—	94	4	no	—
502	D₄	—	188	2	no	—
503	D₄	—	188	2	no	—
504	D₄	—	188	2	no	—
505	D₄	—	188	2	no	—
506	D₄	—	188	2	no	—
507	D₄	—	188	2	no	—
508	C₂×C₄	—	94	4	no	—
509	C₂×C₄	—	376	2	no	—
510	C₂×C₄	—	376	2	no	—
511	C₂×C₄	—	188	2	no	—
512	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
513	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
514	C₂×C₄	#13093981	1	1	yes	characteristic
515	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
517	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
518	C₂×C₄	#13093992	1	1	yes	characteristic
519	C₂×C₄	#13093994	1	1	yes	characteristic
520	C₂×C₄	#13093994	1	1	yes	characteristic
521	C₂×C₄	#13093996	1	1	yes	characteristic
522	C₂×C₄	#13093997	1	1	yes	characteristic
523	C₂×C₄	#13093997	1	1	yes	characteristic
524	C₂×C₄	#13093997	1	1	yes	characteristic
525	C₂×C₄	#13093997	1	1	yes	characteristic
526	C₂×C₄	#13093997	1	1	yes	characteristic
527	C₂×C₄	#13093998	1	1	yes	characteristic
528	C₂×C₄	#13094002	1	1	yes	characteristic
529	C₂×C₄	#13094002	1	1	yes	characteristic
530	C₂×C₄	#13094002	1	1	yes	characteristic
531	C₂×C₄	#13094002	1	1	yes	characteristic
532	C₂×C₄	#13094004	1	1	yes	characteristic
533	C₂×C₄	#13094006	1	1	yes	characteristic
534	C₂×C₄	#13094007	1	1	yes	characteristic
535	C₂×C₄	#13094010	1	1	yes	characteristic
536	C₂×C₄	#13094010	1	1	yes	characteristic
537	C₂×C₄	#13094012	1	1	yes	characteristic
538	C₂×C₄	#13094018	1	1	yes	characteristic
539	C₂×C₄	#13094020	1	1	yes	characteristic
540	C₈	—	4	2	no	—
541	C₈	—	4	2	no	—
542	C₈	—	4	2	no	—
543	C₈	—	188	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	376	4	no	—
552	C₂²	—	376	4	no	—
553	C₂²	—	376	4	no	—
554	C₂²	—	376	4	no	—
555	C₂²	—	376	4	no	—
556	C₂²	—	376	4	no	—
557	C₂²	—	376	4	no	—
558	C₂²	—	188	4	no	—
559	C₂²	#15688994	1	1	yes	characteristic
560	C₂²	#15689001	1	1	yes	characteristic
561	C₂²	#15689012	1	1	yes	characteristic
562	C₂²	#15689041	1	1	yes	characteristic
563	C₂²	#15689045	1	1	yes	characteristic
564	C₂²	#15689052	1	1	yes	characteristic
565	C₂²	#15689058	1	1	yes	characteristic
566	C₄	—	376	2	no	—
567	C₄	—	188	4	no	—
568	C₄	#15688982	1	1	yes	characteristic
569	C₄	#15688997	1	1	yes	characteristic
570	C₄	#15689014	1	1	yes	characteristic
571	C₄	#15689023	1	1	yes	characteristic
572	C₄	#15689032	1	1	yes	characteristic
573	C₄	#15689036	1	1	yes	characteristic
574	C₄	#15689038	1	1	yes	characteristic
575	C₄	#15689047	1	1	yes	characteristic
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	1	no	—
579	C₂	—	2	1	no	—
580	C₂	—	2	1	no	—
581	C₂	—	2	1	no	—
582	C₂	—	376	4	no	—
583	C₂	#20241632	1	1	yes	characteristic
584	C₂	#20243869	1	2	yes	—

	subgroup	G/H
center	C₂²	#15689001
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#338	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂³×D₁₈₈	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#338	D₄₇
hypocenter	C₄₇	#11058
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#338

Complements

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

N	H ≅ G/N	type
1. #20251951	C₂	semidirect
5. C₂×#15688894	C₂	semidirect
6. #20243099	C₂	semidirect
7. C₂×C₄₇×#338	C₂	semidirect
20. C₂×#13093946	C₄	semidirect
290. C₂×#338	D₄₇	semidirect
322. C₄₇	#11058	semidirect

Maximal subgroups

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

subgroup	index
#20251951	2
C₂×#15689129	2
C₂²×#13093940	2
C₂×#15688894	2
#20243099	2
C₂×C₄₇×#338	2
#11058	47