Subgroups — #26232251

Order 12032.

1320 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258162	C₂	1	1	yes	maximal, characteristic
2	#20252306	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094046	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251932	C₂	1	2	yes	maximal, complemented
5	#20244286	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244276	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243888	C₂	1	2	yes	maximal, complemented
8	#20243751	C₂	1	2	yes	maximal, complemented
9	#20243442	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243353	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689959	C₂²	1	2	yes	—
13	#15689940	—	2	1	no	—
14	#15689940	C₄	1	2	yes	complemented
15	#15689935	—	2	2	no	—
16	#15689935	C₄	1	4	yes	complemented
17	#15689928	—	2	1	no	—
18	#15689928	C₄	1	2	yes	complemented
19	#15689923	—	2	2	no	—
20	#15689923	C₂²	1	2	yes	—
21	C₂×#13094046	—	2	2	no	—
22	C₂×#13094046	C₂²	1	1	yes	characteristic
23	C₂×#13094046	C₂²	1	1	yes	characteristic
24	#15689889	C₂²	1	2	yes	complemented
25	C₄×#10625350	C₂²	1	2	yes	complemented
26	#15689246	—	2	2	no	—
27	#15689241	—	2	2	no	—
28	C₄×Dic₁₈₈	—	2	1	no	—
29	C₄×#10625325	—	2	2	no	—
30	C₄×D₃₇₆	—	2	1	no	—
31	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
32	#15689161	C₂²	1	1	yes	characteristic, complemented
33	#15689141	C₂²	1	2	yes	complemented
34	#15689140	C₂²	1	2	yes	—
35	#15689139	C₂²	1	2	yes	complemented
36	#15689138	—	2	4	no	—
37	C₂×#13093952	C₂²	1	2	yes	complemented
38	#104×D₄₇	—	2	4	no	—
39	#15689120	C₂²	1	2	yes	complemented
40	#15689096	C₂²	1	2	yes	complemented
41	#15689089	C₂²	1	2	yes	complemented
42	#15688895	C₂²	1	2	yes	complemented
43	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#416	C₂²	1	1	yes	characteristic
46	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
48	C₄₇×#341	C₂²	1	1	yes	characteristic, complemented
49	C₄₇×#339	C₂²	1	1	yes	characteristic, complemented
50	#13094072	—	2	2	no	—
51	#13094071	—	2	2	no	—
52	#13094071	C₂×C₄	1	4	yes	complemented
53	#13094070	—	2	2	no	—
54	#13094070	C₂×C₄	1	4	yes	complemented
55	#13094069	—	2	2	no	—
56	#13094069	—	4	2	no	—
57	C₂×#10625350	—	2	4	no	—
58	C₂×#10625350	C₂³	1	2	yes	—
59	C₂×#10625350	C₂³	1	2	yes	—
60	#41×D₄₇	—	2	4	no	—
61	#41×D₄₇	—	4	2	no	—
62	#13094057	—	2	2	no	—
63	#13094057	—	2	4	no	—
64	#13094057	—	2	4	no	—
65	#13094057	C₂×C₄	1	4	yes	complemented
66	#13094052	—	2	2	no	—
67	#13094052	—	2	4	no	—
68	#13094052	—	2	4	no	—
69	#13094052	C₂×C₄	1	4	yes	complemented
70	#13094046	—	2	4	no	—
71	#13094046	—	2	1	no	—
72	#13094046	—	2	1	no	—
73	#13094046	—	2	1	no	—
74	#13094046	—	2	1	no	—
75	#13094046	—	2	2	no	—
76	#13094046	—	2	2	no	—
77	#13094046	—	2	4	no	—
78	#13094046	C₂×C₄	1	2	yes	—
79	#13094046	C₂×C₄	1	2	yes	—
80	#13094046	D₄	1	2	yes	—
81	#13094046	D₄	1	2	yes	—
82	C₂×Dic₁₈₈	—	2	2	no	—
83	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂×Dic₁₈₈	D₄	1	1	yes	characteristic
85	C₂×#10625325	—	2	4	no	—
86	C₂×#10625325	C₂×C₄	1	2	yes	complemented
87	C₂×#10625325	D₄	1	2	yes	—
88	C₂×D₃₇₆	—	2	2	no	—
89	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂×D₃₇₆	D₄	1	1	yes	characteristic
91	#13094032	—	4	2	no	—
92	#13094030	—	2	4	no	—
93	C₂×#10625329	C₂³	1	2	yes	—
94	M₁₆×D₄₇	—	2	4	no	—
95	C₄×Dic₉₄	—	2	2	no	—
96	C₄×D₁₈₈	—	2	2	no	—
97	C₄×C₂²⋊D₄₇	—	4	2	no	—
98	#13093983	C₂³	1	2	yes	—
99	#13093981	—	2	2	no	—
100	C₄²×D₄₇	—	2	2	no	—
101	#13093960	—	2	1	no	—
102	#13093960	—	2	1	no	—
103	#13093958	—	2	1	no	—
104	#13093956	—	2	1	no	—
105	#13093952	—	2	4	no	—
106	#13093952	—	2	2	no	—
107	#13093952	—	2	2	no	—
108	#13093951	—	2	4	no	—
109	#13093950	—	2	4	no	—
110	#13093949	—	2	2	no	—
111	#13093946	—	2	2	no	—
112	#13093938	—	4	2	no	—
113	(C₂×D₄₇)⋊C₈	—	4	2	no	—
114	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
115	#131×C₄₇	—	2	1	no	—
116	#131×C₄₇	—	2	1	no	—
117	#131×C₄₇	C₂×C₄	1	2	yes	complemented
118	#131×C₄₇	C₂×C₄	1	2	yes	complemented
119	C₂×M₁₆×C₄₇	—	2	1	no	—
120	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	—	2	1	no	—
123	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	#117×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	#104×C₄₇	D₄	1	2	yes	—
128	#104×C₄₇	D₄	1	2	yes	—
129	#103×C₄₇	—	2	1	no	—
130	#102×C₄₇	—	2	1	no	—
131	#97×C₄₇	—	2	1	no	—
132	C₄×C₈×C₄₇	—	2	1	no	—
133	C₄×C₈×C₄₇	—	2	1	no	—
134	C₄×C₈×C₄₇	—	2	1	no	—
135	#41×C₄₇	—	2	1	no	—
136	#41×C₄₇	—	2	1	no	—
137	#41×C₄₇	C₂²×C₄	1	2	yes	—
138	#41×C₄₇	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₄₇	#41	1	1	yes	characteristic
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	#41	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	—	2	1	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂×C₂²⋊D₄₇	—	2	2	no	—
146	C₂×C₂²⋊D₄₇	—	2	2	no	—
147	C₂×C₂²⋊D₄₇	—	4	4	no	—
148	#10625354	—	2	4	no	—
149	#10625354	—	4	2	no	—
150	Q₈×D₄₇	—	2	4	no	—
151	Q₈×D₄₇	—	4	2	no	—
152	#10625352	—	2	4	no	—
153	#10625352	—	4	2	no	—
154	#10625352	—	4	4	no	—
155	#10625352	—	4	4	no	—
156	D₄×D₄₇	—	2	4	no	—
157	D₄×D₄₇	—	4	2	no	—
158	D₄×D₄₇	—	4	4	no	—
159	D₄×D₄₇	—	4	4	no	—
160	#10625350	—	2	2	no	—
161	#10625350	—	2	2	no	—
162	#10625350	—	2	2	no	—
163	#10625350	—	2	2	no	—
164	#10625350	—	2	2	no	—
165	#10625350	—	2	2	no	—
166	#10625350	—	2	4	no	—
167	#10625350	—	2	4	no	—
168	#10625350	—	4	4	no	—
169	#10625350	—	4	4	no	—
170	#10625350	C₂²×C₄	1	4	yes	—
171	#10625350	C₂×D₄	1	4	yes	—
172	C₂×D₁₈₈	—	2	4	no	—
173	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
174	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
175	C₂×C₄×D₄₇	—	2	2	no	—
176	C₂×C₄×D₄₇	—	2	2	no	—
177	C₂×C₄×D₄₇	—	4	4	no	—
178	C₂×C₄×D₄₇	—	4	2	no	—
179	C₂×Dic₉₄	—	2	4	no	—
180	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
181	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
182	M₁₆×C₄₇	—	2	1	no	—
183	M₁₆×C₄₇	—	2	1	no	—
184	M₁₆×C₄₇	—	2	2	no	—
185	M₁₆×C₄₇	—	2	2	no	—
186	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
187	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₄₇	—	2	1	no	—
189	C₂×C₈×C₄₇	—	2	1	no	—
190	C₂×C₈×C₄₇	—	2	2	no	—
191	C₂×C₈×C₄₇	—	2	2	no	—
192	C₂×C₈×C₄₇	—	2	1	no	—
193	C₂×C₈×C₄₇	—	2	1	no	—
194	C₂×C₈×C₄₇	—	2	1	no	—
195	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
196	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₄₇	—	2	1	no	—
202	C₂²⋊C₄×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	—	2	1	no	—
205	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²⋊Dic₄₇	—	2	2	no	—
208	(C₂×D₄₇)⋊C₄	—	4	2	no	—
209	C₄⋊Dic₄₇	—	2	2	no	—
210	Dic₄₇⋊C₄	—	4	2	no	—
211	C₄×Dic₄₇	—	2	2	no	—
212	C₄×Dic₄₇	—	4	2	no	—
213	#10625329	—	2	2	no	—
214	#10625329	—	2	2	no	—
215	C₂×C₄₇⋊C₈	—	2	2	no	—
216	Dic₁₈₈	—	2	4	no	—
217	Dic₁₈₈	—	2	1	no	—
218	Dic₁₈₈	—	2	1	no	—
219	Dic₁₈₈	C₂²⋊C₄	1	2	yes	—
220	Dic₁₈₈	C₂²⋊C₄	1	2	yes	—
221	D₃₇₆	—	2	4	no	—
222	D₃₇₆	—	2	1	no	—
223	D₃₇₆	—	2	1	no	—
224	D₃₇₆	C₂²⋊C₄	1	2	yes	—
225	D₃₇₆	C₂²⋊C₄	1	2	yes	—
226	#10625325	—	2	4	no	—
227	#10625325	—	2	4	no	—
228	#10625325	—	2	2	no	—
229	#10625325	—	2	2	no	—
230	#10625325	C₂²⋊C₄	1	4	yes	—
231	#10625325	C₂²⋊C₄	1	4	yes	—
232	#10625324	—	4	4	no	—
233	C₈×D₄₇	—	4	4	no	—
234	C₂³×C₄₇	—	2	1	no	—
235	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²×D₄₇	—	2	2	no	—
237	C₂²×D₄₇	—	2	2	no	—
238	C₂²×D₄₇	—	4	4	no	—
239	Q₈×C₄₇	—	2	1	no	—
240	Q₈×C₄₇	C₄×D₄	1	2	yes	—
241	D₄×C₄₇	—	2	2	no	—
242	D₄×C₄₇	—	2	2	no	—
243	D₄×C₄₇	—	2	1	no	—
244	D₄×C₄₇	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂²⋊D₄₇	—	2	4	no	—
260	C₂²⋊D₄₇	—	4	4	no	—
261	C₂²⋊D₄₇	—	4	4	no	—
262	C₂²⋊D₄₇	—	4	2	no	—
263	C₂²⋊D₄₇	—	4	2	no	—
264	C₂×Dic₄₇	—	2	2	no	—
265	C₂×Dic₄₇	—	2	2	no	—
266	C₂×Dic₄₇	—	4	4	no	—
267	C₂×Dic₄₇	—	4	2	no	—
268	D₁₈₈	—	2	2	no	—
269	D₁₈₈	—	2	2	no	—
270	D₁₈₈	—	2	2	no	—
271	D₁₈₈	—	4	4	no	—
272	D₁₈₈	C₂×C₂²⋊C₄	1	4	yes	—
273	C₄×D₄₇	—	2	4	no	—
274	C₄×D₄₇	—	2	4	no	—
275	C₄×D₄₇	—	4	4	no	—
276	C₄×D₄₇	—	4	4	no	—
277	C₄×D₄₇	—	4	2	no	—
278	C₄×D₄₇	—	4	2	no	—
279	C₄×D₄₇	—	8	4	no	—
280	Dic₉₄	—	2	2	no	—
281	Dic₉₄	—	2	2	no	—
282	Dic₉₄	—	2	2	no	—
283	Dic₉₄	—	4	4	no	—
284	Dic₉₄	C₂×C₂²⋊C₄	1	4	yes	—
285	C₈×C₄₇	—	2	2	no	—
286	C₈×C₄₇	—	2	2	no	—
287	C₈×C₄₇	—	4	1	no	—
288	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₄₇⋊C₈	—	4	2	no	—
293	#22462	—	47	1	no	maximal, Sylow
294	C₂²×C₄₇	—	2	2	no	—
295	C₂²×C₄₇	—	4	1	no	—
296	C₂²×C₄₇	—	8	1	no	—
297	C₂²×C₄₇	#518	1	1	yes	characteristic
298	C₂²×C₄₇	D₄²	1	1	yes	characteristic
299	C₂²×C₄₇	#546	1	1	yes	characteristic
300	C₂×D₄₇	—	2	4	no	—
301	C₂×D₄₇	—	4	2	no	—
302	C₂×D₄₇	—	8	2	no	—
303	C₂×D₄₇	—	8	2	no	—
304	C₂×D₄₇	—	16	4	no	—
305	C₄×C₄₇	—	2	2	no	—
306	C₄×C₄₇	—	2	2	no	—
307	C₄×C₄₇	—	4	1	no	—
308	C₄×C₄₇	—	8	1	no	—
309	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
310	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
311	C₄×C₄₇	D₄²	1	1	yes	characteristic
312	C₄×C₄₇	#546	1	1	yes	characteristic
313	Dic₄₇	—	2	4	no	—
314	Dic₄₇	—	4	2	no	—
315	Dic₄₇	—	8	2	no	—
316	#3584	—	47	1	no	—
317	#2957	—	47	1	no	—
318	C₄×#135	—	47	1	no	—
319	#2901	—	47	2	no	—
320	#1976	—	47	1	no	—
321	#1974	—	47	1	no	—
322	#1906	—	47	2	no	—
323	#1881	—	47	2	no	—
324	#1814	—	47	1	no	—
325	#1794	—	47	2	no	—
326	#1764	D₄₇	1	1	yes	characteristic, complemented
327	C₂×C₄₇	—	2	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	—	2	1	no	—
330	C₂×C₄₇	—	4	2	no	—
331	C₂×C₄₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
332	D₄₇	—	4	4	no	—
333	D₄₇	—	8	2	no	—
334	#585	—	47	2	no	—
335	#578	—	47	2	no	—
336	#578	—	94	1	no	—
337	#577	—	47	4	no	—
338	#577	—	94	2	no	—
339	#576	—	47	2	no	—
340	#576	—	94	1	no	—
341	#575	—	47	2	no	—
342	#575	—	94	2	no	—
343	C₂×#135	—	47	1	no	—
344	C₂×#135	—	47	1	no	—
345	C₂×#135	—	94	2	no	—
346	#568	—	47	2	no	—
347	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
348	C₄×#41	—	47	2	no	—
349	#444	—	94	2	no	—
350	#443	—	94	2	no	—
351	C₄×Q₁₆	—	94	1	no	—
352	C₄×SD₁₆	—	94	2	no	—
353	C₄×D₈	—	94	1	no	—
354	C₂×#108	—	47	1	no	—
355	#427	—	47	1	no	—
356	#421	—	47	2	no	—
357	#421	—	47	2	no	—
358	#421	—	47	2	no	—
359	#421	—	94	4	no	—
360	C₂×#104	—	47	2	no	—
361	C₂×#104	—	94	4	no	—
362	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
363	#416	—	47	2	no	—
364	#416	C₂×D₄₇	1	1	yes	characteristic
365	#410	—	47	2	no	—
366	#408	—	47	2	no	—
367	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
368	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
369	#344	—	47	2	no	—
370	#341	C₂×D₄₇	1	1	yes	characteristic, complemented
371	#339	C₂×D₄₇	1	1	yes	characteristic, complemented
372	C₄₇	#22462	1	1	yes	characteristic, complemented, Sylow
373	2₋¹⁺⁴	—	47	4	no	—
374	2₋¹⁺⁴	—	94	2	no	—
375	2₋¹⁺⁴	—	94	2	no	—
376	H(5,𝔽₂)	—	47	4	no	—
377	H(5,𝔽₂)	—	94	2	no	—
378	H(5,𝔽₂)	—	94	2	no	—
379	H(5,𝔽₂)	—	188	2	no	—
380	C₂×#41	—	47	2	no	—
381	C₂×#41	—	47	2	no	—
382	C₂×#41	—	94	4	no	—
383	C₂×#41	—	94	4	no	—
384	C₂×#41	—	188	2	no	—
385	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
386	#137	—	47	4	no	—
387	#137	—	94	4	no	—
388	#137	—	94	4	no	—
389	#137	—	94	2	no	—
390	AGL(1,ℤ/8)	—	47	4	no	—
391	AGL(1,ℤ/8)	—	94	4	no	—
392	AGL(1,ℤ/8)	—	94	4	no	—
393	AGL(1,ℤ/8)	—	94	2	no	—
394	#135	—	47	2	no	—
395	#135	—	47	2	no	—
396	#135	—	47	2	no	—
397	#135	—	47	2	no	—
398	#135	—	94	2	no	—
399	#135	—	94	4	no	—
400	#135	—	94	2	no	—
401	#135	—	94	4	no	—
402	#135	—	94	1	no	—
403	#135	—	94	1	no	—
404	#135	—	94	1	no	—
405	#135	—	94	1	no	—
406	C₂×Q₁₆	—	47	1	no	—
407	C₂×Q₁₆	—	47	1	no	—
408	C₂×Q₁₆	—	94	2	no	—
409	C₂×SD₁₆	—	47	2	no	—
410	C₂×SD₁₆	—	47	2	no	—
411	C₂×SD₁₆	—	94	4	no	—
412	C₂×D₈	—	47	1	no	—
413	C₂×D₈	—	47	1	no	—
414	C₂×D₈	—	94	2	no	—
415	#131	—	2	1	no	—
416	#131	—	2	1	no	—
417	#131	—	94	4	no	—
418	#131	—	188	2	no	—
419	#131	C₄×D₄₇	1	2	yes	complemented
420	#131	C₄×D₄₇	1	2	yes	complemented
421	C₂×M₁₆	—	2	1	no	—
422	C₂×M₁₆	—	47	2	no	—
423	C₂×M₁₆	—	94	4	no	—
424	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
425	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
428	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
429	C₄×Q₈	—	94	2	no	—
430	C₄×D₄	—	94	2	no	—
431	C₄×D₄	—	188	2	no	—
432	#117	—	47	2	no	—
433	#117	—	94	2	no	—
434	#117	C₂²×D₄₇	1	1	yes	characteristic
435	C₂×C₄²	—	94	2	no	—
436	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
437	#108	—	94	1	no	—
438	#108	—	94	1	no	—
439	#107	—	94	1	no	—
440	#106	—	94	1	no	—
441	#104	—	94	4	no	—
442	#104	—	94	4	no	—
443	#104	—	94	4	no	—
444	#104	—	94	2	no	—
445	#104	—	94	2	no	—
446	#104	D₁₈₈	1	2	yes	—
447	#104	D₁₈₈	1	2	yes	—
448	#103	—	2	1	no	—
449	#103	—	94	2	no	—
450	#102	—	2	1	no	—
451	#102	—	94	2	no	—
452	#99	—	188	2	no	—
453	C₂²⋊C₈	—	188	2	no	—
454	#97	—	2	1	no	—
455	C₄×C₈	—	2	1	no	—
456	C₄×C₈	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	#41	—	2	1	no	—
459	#41	—	2	1	no	—
460	#41	—	47	4	no	—
461	#41	—	47	4	no	—
462	#41	—	94	4	no	—
463	#41	—	94	4	no	—
464	#41	—	94	2	no	—
465	#41	—	94	2	no	—
466	#41	—	94	4	no	—
467	#41	—	94	4	no	—
468	#41	—	94	2	no	—
469	#41	—	94	2	no	—
470	#41	—	94	2	no	—
471	#41	—	94	2	no	—
472	#41	—	188	4	no	—
473	#41	—	188	4	no	—
474	#41	—	188	4	no	—
475	#41	—	188	4	no	—
476	#41	—	188	2	no	—
477	#41	—	188	2	no	—
478	#41	C₂×C₄×D₄₇	1	2	yes	—
479	#41	C₂×D₁₈₈	1	2	yes	—
480	C₂×Q₈	—	47	2	no	—
481	C₂×Q₈	—	47	2	no	—
482	C₂×Q₈	—	94	4	no	—
483	C₂×Q₈	—	94	4	no	—
484	C₂×Q₈	—	188	2	no	—
485	C₂×Q₈	#10625350	1	1	yes	characteristic
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	47	2	no	—
488	C₂×D₄	—	47	2	no	—
489	C₂×D₄	—	94	4	no	—
490	C₂×D₄	—	94	2	no	—
491	C₂×D₄	—	94	4	no	—
492	C₂×D₄	—	94	2	no	—
493	C₂×D₄	—	188	4	no	—
494	C₂×D₄	—	188	2	no	—
495	C₂×D₄	—	188	4	no	—
496	C₂×D₄	—	188	4	no	—
497	C₂×D₄	#10625350	1	1	yes	characteristic
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	94	2	no	—
501	C₂²×C₄	—	94	2	no	—
502	C₂²×C₄	—	188	4	no	—
503	C₂²×C₄	—	188	2	no	—
504	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
505	Q₁₆	—	47	2	no	—
506	Q₁₆	—	47	2	no	—
507	Q₁₆	—	94	4	no	—
508	Q₁₆	—	94	1	no	—
509	Q₁₆	—	94	1	no	—
510	SD₁₆	—	47	4	no	—
511	SD₁₆	—	47	4	no	—
512	SD₁₆	—	94	4	no	—
513	SD₁₆	—	94	4	no	—
514	SD₁₆	—	94	2	no	—
515	SD₁₆	—	94	2	no	—
516	D₈	—	47	2	no	—
517	D₈	—	47	2	no	—
518	D₈	—	94	4	no	—
519	D₈	—	94	1	no	—
520	D₈	—	94	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	2	2	no	—
524	M₁₆	—	2	2	no	—
525	M₁₆	—	94	2	no	—
526	M₁₆	—	94	2	no	—
527	M₁₆	—	188	4	no	—
528	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
529	M₁₆	C₂×D₁₈₈	1	2	yes	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	2	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	94	2	no	—
538	C₂×C₈	—	188	4	no	—
539	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
540	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
541	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
542	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
543	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
544	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	94	2	no	—
547	C₄⋊C₄	—	188	2	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	94	2	no	—
550	C₂²⋊C₄	—	188	2	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	94	2	no	—
554	C₄²	—	188	2	no	—
555	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
556	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
557	C₂³	—	2	1	no	—
558	C₂³	—	94	2	no	—
559	C₂³	—	94	2	no	—
560	C₂³	—	188	4	no	—
561	C₂³	#13094070	1	1	yes	characteristic
562	Q₈	—	2	1	no	—
563	Q₈	—	47	4	no	—
564	Q₈	—	94	2	no	—
565	Q₈	—	94	2	no	—
566	Q₈	—	94	2	no	—
567	Q₈	—	188	4	no	—
568	Q₈	C₄×D₁₈₈	1	2	yes	—
569	D₄	—	2	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	2	1	no	—
572	D₄	—	47	4	no	—
573	D₄	—	94	4	no	—
574	D₄	—	94	4	no	—
575	D₄	—	94	2	no	—
576	D₄	—	94	2	no	—
577	D₄	—	94	2	no	—
578	D₄	—	188	4	no	—
579	D₄	—	188	4	no	—
580	D₄	—	188	4	no	—
581	D₄	—	188	2	no	—
582	D₄	—	188	2	no	—
583	D₄	C₄×D₁₈₈	1	2	yes	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	94	2	no	—
592	C₂×C₄	—	94	4	no	—
593	C₂×C₄	—	94	4	no	—
594	C₂×C₄	—	94	2	no	—
595	C₂×C₄	—	376	4	no	—
596	C₂×C₄	—	188	4	no	—
597	C₂×C₄	—	188	4	no	—
598	C₂×C₄	—	188	4	no	—
599	C₂×C₄	—	188	2	no	—
600	C₂×C₄	—	188	2	no	—
601	C₂×C₄	—	188	2	no	—
602	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
603	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
604	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
606	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
607	C₂×C₄	#13094070	1	1	yes	characteristic
608	C₈	—	2	2	no	—
609	C₈	—	2	2	no	—
610	C₈	—	4	1	no	—
611	C₈	—	188	2	no	—
612	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
613	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
614	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
615	C₈	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
616	C₂²	—	2	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	94	4	no	—
620	C₂²	—	376	2	no	—
621	C₂²	—	376	2	no	—
622	C₂²	—	188	2	no	—
623	C₂²	—	752	4	no	—
624	C₂²	#15689597	1	1	yes	characteristic
625	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
626	C₂²	#15689769	1	1	yes	characteristic
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	8	1	no	—
631	C₄	—	94	4	no	—
632	C₄	—	376	2	no	—
633	C₄	—	188	2	no	—
634	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
635	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
636	C₄	D₄×D₁₈₈	1	1	yes	characteristic
637	C₄	#15689769	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	4	2	no	—
642	C₂	—	376	2	no	—
643	C₂	—	188	4	no	—
644	C₂	C₂²⋊C₄×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1764	C₂
socle	C₂×C₄₇	D₄×C₂²⋊C₄
prime radical	#20258162	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1764	D₄₇
hypocenter	C₄₇	#22462
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #20252306	C₂	semidirect
3. C₄×#13094046	C₂	semidirect
4. #20251932	C₂	semidirect
5. #20244286	C₂	semidirect
6. #20244276	C₂	semidirect
7. #20243888	C₂	semidirect
8. #20243751	C₂	semidirect
9. #20243442	C₂	semidirect
10. #20243353	C₂	semidirect
11. C₄₇×#1764	C₂	semidirect
14. #15689940	C₄	semidirect
16. #15689935	C₄	semidirect
18. #15689928	C₄	semidirect
24. #15689889	C₂²	semidirect
25. C₄×#10625350	C₂²	semidirect
31. C₂×#13093960	C₂²	semidirect
32. #15689161	C₂²	semidirect
33. #15689141	C₂²	semidirect
35. #15689139	C₂²	semidirect
37. C₂×#13093952	C₂²	semidirect
39. #15689120	C₂²	semidirect
40. #15689096	C₂²	semidirect
41. #15689089	C₂²	semidirect
42. #15688895	C₂²	semidirect
46. C₄₇×#405	C₂²	semidirect
47. C₂×C₄×C₈×C₄₇	C₂²	semidirect
48. C₄₇×#341	C₂²	semidirect
49. C₄₇×#339	C₂²	semidirect
52. #13094071	C₂×C₄	semidirect
54. #13094070	C₂×C₄	semidirect
65. #13094057	C₂×C₄	semidirect
69. #13094052	C₂×C₄	semidirect
83. C₂×Dic₁₈₈	C₂×C₄	semidirect
86. C₂×#10625325	C₂×C₄	semidirect
89. C₂×D₃₇₆	C₂×C₄	semidirect
117. #131×C₄₇	C₂×C₄	semidirect
118. #131×C₄₇	C₂×C₄	semidirect
326. #1764	D₄₇	semidirect
367. #405	C₂×D₄₇	semidirect
368. C₂×C₄×C₈	C₂×D₄₇	semidirect
370. #341	C₂×D₄₇	semidirect
371. #339	C₂×D₄₇	semidirect
372. C₄₇	#22462	semidirect
419. #131	C₄×D₄₇	semidirect
420. #131	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20258162	2
#20252306	2
C₄×#13094046	2
#20251932	2
#20244286	2
#20244276	2
#20243888	2
#20243751	2
#20243442	2
#20243353	2
C₄₇×#1764	2
#22462	47