Subgroups — #26222724

Order 12032.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252845	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689241	C₂	1	2	yes	maximal, complemented
3	#20252101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13094030	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244306	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244037	C₂	1	2	yes	maximal, complemented
8	#20243714	C₂	1	2	yes	maximal, complemented
9	#20243409	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243225	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	2	yes	—
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	C₂×#13094030	C₂²	1	2	yes	—
15	C₂×#13094030	C₂²	1	1	yes	characteristic
16	#15689673	C₂²	1	1	yes	characteristic
17	C₄×#10625350	C₂²	1	1	yes	characteristic
18	#15689346	C₄	1	2	yes	complemented
19	#15689339	C₄	1	2	yes	complemented
20	#15689334	C₄	1	1	yes	characteristic, complemented
21	#15689329	C₄	1	1	yes	characteristic, complemented
22	#15689324	C₄	1	1	yes	characteristic, complemented
23	#15689319	C₄	1	1	yes	characteristic, complemented
24	#15689241	—	2	8	no	—
25	#15689202	—	2	1	no	—
26	#15689202	—	2	1	no	—
27	C₈×D₁₈₈	—	2	1	no	—
28	C₈×D₁₈₈	—	2	1	no	—
29	C₂×#13093960	C₂²	1	2	yes	—
30	#15689147	C₂²	1	1	yes	characteristic
31	C₂×#13093952	C₂²	1	2	yes	—
32	C₂×#13093952	C₂²	1	2	yes	—
33	C₂×#13093952	C₂²	1	2	yes	—
34	#15689120	C₂²	1	2	yes	—
35	#15689089	C₂²	1	2	yes	—
36	#15689078	C₂²	1	1	yes	characteristic
37	#15689078	C₂²	1	1	yes	characteristic
38	#15689077	—	2	1	no	—
39	#15689077	—	2	1	no	—
40	C₄×#10625329	C₂²	1	1	yes	characteristic
41	C₄×#10625324	—	2	1	no	—
42	C₄×C₈×D₄₇	—	2	1	no	—
43	#15688888	C₂²	1	2	yes	—
44	#15688883	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
49	C₄₇×#336	C₂²	1	2	yes	—
50	C₂×#10625350	C₂³	1	2	yes	—
51	C₂×#10625350	C₂³	1	1	yes	characteristic
52	#13094046	—	2	4	no	—
53	#13094046	—	2	4	no	—
54	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
55	C₂×#10625325	C₂×C₄	1	2	yes	—
56	C₂×#10625325	C₂×C₄	1	2	yes	—
57	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
58	#13094030	—	2	2	no	—
59	#13094030	—	2	2	no	—
60	#13094030	—	2	2	no	—
61	#13094030	—	2	4	no	—
62	#13094030	—	2	4	no	—
63	#13094030	D₄	1	4	yes	complemented
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂×#10625329	C₂³	1	1	yes	characteristic
66	C₂×#10625329	C₂³	1	1	yes	characteristic
67	C₂×#10625324	—	2	1	no	—
68	C₂×#10625324	—	2	1	no	—
69	C₂×#10625324	—	2	2	no	—
70	C₂×C₈×D₄₇	—	2	1	no	—
71	C₂×C₈×D₄₇	—	2	1	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	#13094024	C₂×C₄	1	1	yes	characteristic
74	#13094021	C₂×C₄	1	1	yes	characteristic
75	#13094012	C₂×C₄	1	2	yes	—
76	#13093998	—	2	1	no	—
77	#13093998	—	2	1	no	—
78	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
80	C₄×D₁₈₈	—	2	1	no	—
81	C₄×D₁₈₈	—	2	1	no	—
82	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
83	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₄₇	—	2	1	no	—
85	C₄×C₂²⋊D₄₇	—	2	1	no	—
86	#13093983	C₂³	1	1	yes	characteristic
87	#13093981	—	2	1	no	—
88	C₄²×D₄₇	—	2	1	no	—
89	#13093960	—	2	4	no	—
90	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
91	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
92	#13093952	—	2	4	no	—
93	#13093952	—	2	4	no	—
94	#13093952	—	2	4	no	—
95	#13093949	C₂×C₄	1	2	yes	—
96	#13093949	C₂×C₄	1	2	yes	—
97	#13093946	C₂×C₄	1	2	yes	—
98	#13093946	C₂×C₄	1	2	yes	—
99	(C₂×D₄₇)⋊C₈	—	2	2	no	—
100	(C₂×D₄₇)⋊C₈	—	2	2	no	—
101	#13093935	—	2	1	no	—
102	#13093934	—	2	1	no	—
103	#13093934	—	2	1	no	—
104	C₄×C₄₇⋊C₈	—	2	1	no	—
105	C₈×Dic₄₇	—	2	1	no	—
106	C₈×Dic₄₇	—	2	1	no	—
107	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
108	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
116	C₄×C₈×C₄₇	—	2	4	no	—
117	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
118	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
119	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
120	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
121	#95×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₇	—	2	1	no	—
127	C₂×C₂²⋊D₄₇	—	2	2	no	—
128	#10625350	—	2	1	no	—
129	#10625350	—	2	1	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	2	2	no	—
132	#10625350	—	2	2	no	—
133	#10625350	—	2	2	no	—
134	#10625350	C₂×D₄	1	2	yes	—
135	#10625350	#41	1	2	yes	—
136	C₂×D₁₈₈	—	2	1	no	—
137	C₂×D₁₈₈	—	2	1	no	—
138	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
139	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₄₇	—	2	1	no	—
141	C₂×C₄×D₄₇	—	2	1	no	—
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	2	2	no	—
144	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
145	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₇	#41	1	2	yes	—
158	C₄⋊C₄×C₄₇	—	2	4	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²⋊Dic₄₇	—	2	1	no	—
166	(C₂×D₄₇)⋊C₄	—	2	1	no	—
167	(C₂×D₄₇)⋊C₄	—	2	1	no	—
168	(C₂×D₄₇)⋊C₄	—	2	2	no	—
169	(C₂×D₄₇)⋊C₄	—	2	2	no	—
170	C₄⋊Dic₄₇	—	2	1	no	—
171	C₄⋊Dic₄₇	—	2	1	no	—
172	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
174	Dic₄₇⋊C₄	—	2	1	no	—
175	Dic₄₇⋊C₄	—	2	1	no	—
176	C₄×Dic₄₇	—	2	1	no	—
177	C₄×Dic₄₇	—	2	1	no	—
178	C₄×Dic₄₇	—	2	1	no	—
179	#10625329	—	2	1	no	—
180	#10625329	—	2	1	no	—
181	#10625329	—	2	2	no	—
182	#10625329	—	2	2	no	—
183	#10625329	C₂×D₄	1	2	yes	—
184	#10625329	#41	1	2	yes	—
185	C₂×C₄₇⋊C₈	—	2	1	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	Dic₁₈₈	—	2	4	no	—
189	D₃₇₆	—	2	4	no	—
190	#10625325	—	2	4	no	—
191	#10625325	—	2	4	no	—
192	#10625324	—	2	4	no	—
193	#10625324	—	2	4	no	—
194	#10625324	—	4	4	no	—
195	C₈×D₄₇	—	2	4	no	—
196	C₈×D₄₇	—	2	4	no	—
197	C₈×D₄₇	—	4	4	no	—
198	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂²×D₄₇	—	2	1	no	—
200	C₂²×D₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	4	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂²⋊D₄₇	—	2	2	no	—
217	C₂²⋊D₄₇	—	2	2	no	—
218	C₂²⋊D₄₇	—	4	2	no	—
219	C₂²⋊D₄₇	—	4	2	no	—
220	C₂×Dic₄₇	—	2	1	no	—
221	C₂×Dic₄₇	—	2	1	no	—
222	C₂×Dic₄₇	—	2	1	no	—
223	C₂×Dic₄₇	—	2	2	no	—
224	D₁₈₈	—	2	2	no	—
225	D₁₈₈	—	2	1	no	—
226	D₁₈₈	—	2	2	no	—
227	D₁₈₈	—	4	2	no	—
228	D₁₈₈	—	4	2	no	—
229	D₁₈₈	C₄×D₄	1	2	yes	—
230	C₄×D₄₇	—	2	2	no	—
231	C₄×D₄₇	—	2	2	no	—
232	C₄×D₄₇	—	4	2	no	—
233	C₄×D₄₇	—	4	2	no	—
234	C₄×D₄₇	—	4	2	no	—
235	C₄×D₄₇	—	4	2	no	—
236	Dic₉₄	—	2	1	no	—
237	Dic₉₄	—	2	2	no	—
238	Dic₉₄	—	2	2	no	—
239	Dic₉₄	C₄×D₄	1	2	yes	—
240	C₈×C₄₇	—	2	2	no	—
241	C₈×C₄₇	—	2	2	no	—
242	C₈×C₄₇	—	2	1	no	—
243	C₈×C₄₇	—	2	1	no	—
244	C₈×C₄₇	#121	1	2	yes	—
245	C₈×C₄₇	#121	1	2	yes	—
246	C₄₇⋊C₈	—	2	2	no	—
247	C₄₇⋊C₈	—	2	2	no	—
248	C₄₇⋊C₈	—	4	2	no	—
249	#21517	—	47	1	no	maximal, Sylow
250	C₂²×C₄₇	—	2	1	no	—
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₄₇	#529	1	1	yes	characteristic
254	C₂²×C₄₇	#532	1	1	yes	characteristic
255	C₂×D₄₇	—	2	2	no	—
256	C₂×D₄₇	—	4	1	no	—
257	C₂×D₄₇	—	4	1	no	—
258	C₂×D₄₇	—	4	2	no	—
259	C₂×D₄₇	—	4	2	no	—
260	C₂×D₄₇	—	4	2	no	—
261	C₄×C₄₇	—	2	1	no	—
262	C₄×C₄₇	—	2	1	no	—
263	C₄×C₄₇	—	2	1	no	—
264	C₄×C₄₇	—	4	4	no	—
265	C₄×C₄₇	#443	1	2	yes	complemented
266	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
268	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
269	C₄×C₄₇	#525	1	1	yes	characteristic
270	Dic₄₇	—	2	2	no	—
271	Dic₄₇	—	4	1	no	—
272	Dic₄₇	—	4	1	no	—
273	Dic₄₇	—	4	2	no	—
274	#3035	—	47	1	no	—
275	C₂×#443	—	47	2	no	—
276	#2931	—	47	1	no	—
277	C₄×#131	—	47	1	no	—
278	#1980	—	47	1	no	—
279	#1950	—	47	1	no	—
280	#1929	—	47	2	no	—
281	#1876	—	47	2	no	—
282	#1806	—	47	1	no	—
283	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
284	#1764	—	47	2	no	—
285	C₂×C₄₇	—	2	1	no	—
286	C₂×C₄₇	—	2	1	no	—
287	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
288	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
289	C₂×C₄₇	#2955	1	1	yes	characteristic
290	D₄₇	—	4	2	no	—
291	D₄₇	—	8	2	no	—
292	C₂×#135	—	47	2	no	—
293	C₂×#131	—	47	1	no	—
294	C₂×#131	—	47	1	no	—
295	C₂×#131	—	47	2	no	—
296	#532	—	47	1	no	—
297	C₄×#41	—	47	1	no	—
298	#464	—	47	2	no	—
299	#463	—	47	2	no	—
300	#462	—	47	1	no	—
301	#461	—	47	1	no	—
302	#460	—	47	1	no	—
303	#459	—	47	1	no	—
304	#443	—	94	8	no	—
305	#436	—	94	1	no	—
306	#436	—	94	1	no	—
307	C₈×D₄	—	94	1	no	—
308	C₈×D₄	—	94	1	no	—
309	C₂×#108	—	47	2	no	—
310	#423	—	47	1	no	—
311	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
312	C₂×#104	—	47	2	no	—
313	C₂×#104	—	47	2	no	—
314	C₂×#104	—	47	2	no	—
315	#416	—	47	2	no	—
316	#408	—	47	2	no	—
317	#405	—	47	1	no	—
318	#405	—	47	1	no	—
319	#405	—	94	1	no	—
320	#405	—	94	1	no	—
321	C₄×M₁₆	—	47	1	no	—
322	C₄×M₁₆	—	94	1	no	—
323	C₂×C₄×C₈	—	94	1	no	—
324	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
325	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
327	#341	—	47	2	no	—
328	#339	—	47	2	no	—
329	#336	C₂×D₄₇	1	2	yes	—
330	C₄₇	#21517	1	1	yes	characteristic, complemented, Sylow
331	C₂×#41	—	47	1	no	—
332	C₂×#41	—	47	2	no	—
333	#135	—	94	4	no	—
334	#135	—	94	4	no	—
335	C₂×Q₁₆	—	47	2	no	—
336	C₂×SD₁₆	—	47	2	no	—
337	C₂×SD₁₆	—	47	2	no	—
338	C₂×D₈	—	47	2	no	—
339	#131	—	47	4	no	—
340	#131	—	94	2	no	—
341	#131	—	94	2	no	—
342	#131	—	94	2	no	—
343	#131	—	94	4	no	—
344	#131	—	94	4	no	—
345	C₂×M₁₆	—	47	1	no	—
346	C₂×M₁₆	—	47	1	no	—
347	C₂×M₁₆	—	47	2	no	—
348	C₂×M₁₆	—	94	1	no	—
349	C₂×M₁₆	—	94	1	no	—
350	C₂×M₁₆	—	94	2	no	—
351	C₂²×C₈	—	94	1	no	—
352	C₂²×C₈	—	94	1	no	—
353	C₂²×C₈	—	94	2	no	—
354	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
355	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
357	C₄⋊Q₈	—	47	1	no	—
358	#127	—	47	1	no	—
359	#124	—	47	2	no	—
360	#121	—	94	1	no	—
361	#121	—	94	1	no	—
362	C₄×Q₈	—	47	1	no	—
363	C₄×Q₈	—	47	1	no	—
364	C₄×D₄	—	47	1	no	—
365	C₄×D₄	—	47	1	no	—
366	C₄×D₄	—	94	1	no	—
367	C₄×D₄	—	94	1	no	—
368	C₄×D₄	—	94	1	no	—
369	C₄×D₄	—	94	1	no	—
370	#117	—	47	1	no	—
371	#117	—	94	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	94	1	no	—
374	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
375	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
376	#108	—	94	4	no	—
377	C₄⋊C₈	—	94	1	no	—
378	C₄⋊C₈	—	94	1	no	—
379	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
380	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
381	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
382	#104	—	94	4	no	—
383	#104	—	94	4	no	—
384	#104	—	94	4	no	—
385	#103	—	47	2	no	—
386	#103	—	47	2	no	—
387	#102	—	47	2	no	—
388	#102	—	47	2	no	—
389	C₂²⋊C₈	—	94	2	no	—
390	C₂²⋊C₈	—	94	2	no	—
391	#97	—	94	1	no	—
392	#97	—	94	1	no	—
393	#97	—	94	1	no	—
394	C₄×C₈	—	2	4	no	—
395	C₄×C₈	—	94	1	no	—
396	C₄×C₈	—	94	1	no	—
397	C₄×C₈	—	94	1	no	—
398	C₄×C₈	D₁₈₈	1	1	yes	characteristic
399	C₄×C₈	D₁₈₈	1	1	yes	characteristic
400	C₄×C₈	D₁₈₈	1	1	yes	characteristic
401	C₄×C₈	D₁₈₈	1	1	yes	characteristic
402	#95	—	2	1	no	—
403	#41	—	47	2	no	—
404	#41	—	47	2	no	—
405	#41	—	94	1	no	—
406	#41	—	94	1	no	—
407	#41	—	94	2	no	—
408	#41	—	94	2	no	—
409	#41	—	94	2	no	—
410	#41	—	94	2	no	—
411	C₂×Q₈	—	47	1	no	—
412	C₂×Q₈	—	47	2	no	—
413	C₂×D₄	—	47	1	no	—
414	C₂×D₄	—	47	2	no	—
415	C₂×D₄	—	94	1	no	—
416	C₂×D₄	—	94	2	no	—
417	C₂×D₄	—	94	1	no	—
418	C₂×D₄	—	94	1	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	94	1	no	—
421	C₂²×C₄	—	94	1	no	—
422	C₂²×C₄	—	94	1	no	—
423	C₂²×C₄	—	94	2	no	—
424	C₂²×C₄	#10625350	1	1	yes	characteristic
425	C₂²×C₄	#10625350	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	Q₁₆	—	94	4	no	—
428	SD₁₆	—	94	4	no	—
429	SD₁₆	—	94	4	no	—
430	D₈	—	94	4	no	—
431	M₁₆	—	47	2	no	—
432	M₁₆	—	47	2	no	—
433	M₁₆	—	94	4	no	—
434	M₁₆	—	94	1	no	—
435	M₁₆	—	94	1	no	—
436	M₁₆	—	94	4	no	—
437	M₁₆	—	94	2	no	—
438	M₁₆	—	94	2	no	—
439	M₁₆	—	188	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	94	4	no	—
445	C₂×C₈	—	94	1	no	—
446	C₂×C₈	—	94	1	no	—
447	C₂×C₈	—	94	4	no	—
448	C₂×C₈	—	94	2	no	—
449	C₂×C₈	—	188	4	no	—
450	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
451	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
452	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
453	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
454	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
455	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
456	C₂×C₈	D₄×D₄₇	1	2	yes	—
457	C₂×C₈	#10625354	1	2	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	47	1	no	—
460	C₄⋊C₄	—	47	1	no	—
461	C₄⋊C₄	—	94	1	no	—
462	C₄⋊C₄	—	94	1	no	—
463	C₄⋊C₄	—	94	1	no	—
464	C₄⋊C₄	—	94	1	no	—
465	C₂²⋊C₄	—	94	1	no	—
466	C₂²⋊C₄	—	94	1	no	—
467	C₂²⋊C₄	—	94	1	no	—
468	C₂²⋊C₄	—	94	2	no	—
469	C₂²⋊C₄	—	94	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	2	2	no	—
472	C₄²	—	94	1	no	—
473	C₄²	—	94	1	no	—
474	C₄²	—	94	1	no	—
475	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
477	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
478	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
479	C₂³	—	94	1	no	—
480	C₂³	—	94	2	no	—
481	C₂³	C₂×#10625350	1	1	yes	characteristic
482	Q₈	—	47	2	no	—
483	Q₈	—	94	1	no	—
484	Q₈	—	94	2	no	—
485	Q₈	—	94	2	no	—
486	D₄	—	47	2	no	—
487	D₄	—	94	2	no	—
488	D₄	—	94	2	no	—
489	D₄	—	94	2	no	—
490	D₄	—	94	1	no	—
491	D₄	—	94	2	no	—
492	D₄	—	188	2	no	—
493	D₄	—	188	2	no	—
494	D₄	—	188	2	no	—
495	D₄	—	188	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	94	1	no	—
502	C₂×C₄	—	94	2	no	—
503	C₂×C₄	—	94	2	no	—
504	C₂×C₄	—	94	1	no	—
505	C₂×C₄	—	94	1	no	—
506	C₂×C₄	—	94	2	no	—
507	C₂×C₄	—	188	2	no	—
508	C₂×C₄	—	188	2	no	—
509	C₂×C₄	—	188	2	no	—
510	C₂×C₄	—	188	2	no	—
511	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
512	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
513	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
514	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
518	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
519	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
520	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	94	2	no	—
526	C₈	—	94	2	no	—
527	C₈	—	188	2	no	—
528	C₈	#13093999	1	2	yes	—
529	C₈	#13093999	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	94	2	no	—
533	C₂²	—	188	2	no	—
534	C₂²	—	188	2	no	—
535	C₂²	—	188	2	no	—
536	C₂²	—	188	1	no	—
537	C₂²	—	188	1	no	—
538	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
539	C₂²	#15689660	1	1	yes	characteristic
540	C₂²	#15689670	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	4	no	—
545	C₄	—	94	2	no	—
546	C₄	—	188	1	no	—
547	C₄	—	188	1	no	—
548	C₄	—	188	2	no	—
549	C₄	#15689241	1	2	yes	complemented
550	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
551	C₄	C₄×#10625354	1	1	yes	characteristic
552	C₄	C₂×#13093999	1	1	yes	characteristic
553	C₄	#15689635	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	376	2	no	—
557	C₂	—	188	2	no	—
558	C₂	C₄×#13093999	1	1	yes	characteristic
559	C₂	C₂×#15689241	1	1	yes	characteristic
560	C₂	#20252292	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252845	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#21517
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#15689241	C₂	semidirect
3. #20252101	C₂	semidirect
4. C₄×#13094030	C₂	semidirect
5. #20244306	C₂	semidirect
6. #20244164	C₂	semidirect
7. #20244037	C₂	semidirect
8. #20243714	C₂	semidirect
9. #20243409	C₂	semidirect
10. #20243225	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
18. #15689346	C₄	semidirect
19. #15689339	C₄	semidirect
20. #15689334	C₄	semidirect
21. #15689329	C₄	semidirect
22. #15689324	C₄	semidirect
23. #15689319	C₄	semidirect
63. #13094030	D₄	semidirect
265. C₄×C₄₇	#443	semidirect
283. C₈×C₄⋊C₄	D₄₇	semidirect
330. C₄₇	#21517	semidirect
549. C₄	#15689241	semidirect

Maximal subgroups

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

subgroup	index
#20252845	2
C₂×#15689241	2
#20252101	2
C₄×#13094030	2
#20244306	2
#20244164	2
#20244037	2
#20243714	2
#20243409	2
#20243225	2
C₈×C₄⋊C₄×C₄₇	2
#21517	47