Subgroups — #27092519

Order 12032.

2620 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258162	C₂	1	2	yes	maximal, complemented
2	#20258157	C₂	1	2	yes	maximal, complemented
3	#20255193	C₂	1	2	yes	maximal, complemented
4	#20255188	C₂	1	2	yes	maximal, complemented
5	#20255182	C₂	1	4	yes	maximal, complemented
6	#20255176	C₂	1	4	yes	maximal, complemented
7	#20255175	C₂	1	4	yes	maximal, complemented
8	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
9	#20253109	C₂	1	2	yes	maximal, complemented
10	#20253108	C₂	1	2	yes	maximal, complemented
11	#20252739	C₂	1	4	yes	maximal, complemented
12	C₂×#15689241	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689959	C₂²	1	4	yes	complemented
15	#15689940	—	2	2	no	—
16	#15689940	C₂²	1	4	yes	complemented
17	#15689937	C₂²	1	4	yes	complemented
18	#15689936	—	2	2	no	—
19	#15689935	—	2	4	no	—
20	#15689935	C₂²	1	8	yes	complemented
21	#15689930	C₂²	1	8	yes	complemented
22	#15689929	—	2	4	no	—
23	#15689928	—	2	2	no	—
24	#15689928	C₂²	1	4	yes	complemented
25	#15689925	C₂²	1	4	yes	complemented
26	#15689924	—	2	2	no	—
27	#15689923	—	2	4	no	—
28	#15689923	C₂²	1	4	yes	complemented
29	#15689921	C₂²	1	4	yes	complemented
30	#15689920	—	2	4	no	—
31	C₂×#13094046	—	2	4	no	—
32	C₂×#13094046	C₂²	1	1	yes	characteristic
33	C₂×#13094046	C₂²	1	2	yes	complemented
34	C₂×#13094046	C₂²	1	2	yes	complemented
35	#135×D₄₇	—	2	4	no	—
36	C₂×#13094030	C₂²	1	2	yes	complemented
37	#15689673	C₂²	1	2	yes	complemented
38	#15689507	C₂²	1	2	yes	complemented
39	#15689507	C₂²	1	2	yes	complemented
40	#15689503	C₂²	1	1	yes	characteristic, complemented
41	#15689500	C₂²	1	1	yes	characteristic, complemented
42	#15689496	C₂²	1	2	yes	complemented
43	#15689399	C₂²	1	4	yes	complemented
44	#15689398	C₂²	1	4	yes	complemented
45	#15689394	C₂²	1	4	yes	complemented
46	#15689393	C₂²	1	4	yes	complemented
47	#15689387	C₂²	1	8	yes	complemented
48	#15689386	C₂²	1	8	yes	complemented
49	#15689307	C₂²	1	8	yes	complemented
50	#15689302	C₂²	1	8	yes	complemented
51	#15689297	C₂²	1	8	yes	complemented
52	#15689292	C₂²	1	8	yes	complemented
53	#15689241	C₂²	1	2	yes	complemented
54	#15689241	C₂²	1	2	yes	complemented
55	#15689241	C₂²	1	2	yes	complemented
56	#15689241	C₂²	1	2	yes	complemented
57	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13093952	C₂²	1	2	yes	complemented
59	#15689105	C₂²	1	4	yes	complemented
60	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
61	C₂×#131×C₄₇	C₂²	1	2	yes	complemented
62	C₄₇×#443	C₂²	1	2	yes	complemented
63	C₄₇×#443	C₂²	1	2	yes	complemented
64	C₄₇×#443	C₂²	1	2	yes	complemented
65	C₄₇×#443	C₂²	1	2	yes	complemented
66	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂×#104×C₄₇	C₂²	1	2	yes	complemented
68	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
69	#13094072	—	2	4	no	—
70	#13094071	—	2	4	no	—
71	#13094071	C₂³	1	8	yes	—
72	#13094070	—	2	4	no	—
73	#13094070	C₂³	1	8	yes	—
74	#13094069	—	2	4	no	—
75	#13094069	—	4	4	no	—
76	C₂×#10625350	—	2	8	no	—
77	C₂×#10625350	C₂³	1	2	yes	—
78	C₂×#10625350	C₂³	1	4	yes	—
79	#41×D₄₇	—	2	8	no	—
80	#41×D₄₇	—	4	4	no	—
81	#13094057	—	2	4	no	—
82	#13094057	—	2	8	no	—
83	#13094057	—	2	8	no	—
84	#13094057	C₂³	1	8	yes	—
85	#13094056	—	2	8	no	—
86	#13094055	—	2	4	no	—
87	#13094054	C₂³	1	8	yes	—
88	#13094053	—	2	8	no	—
89	#13094052	—	2	4	no	—
90	#13094052	—	2	8	no	—
91	#13094052	—	2	8	no	—
92	#13094052	C₂³	1	8	yes	—
93	#13094051	—	2	8	no	—
94	#13094050	—	2	4	no	—
95	#13094049	C₂³	1	8	yes	—
96	#13094048	—	2	8	no	—
97	#13094047	—	2	4	no	—
98	#13094046	—	2	8	no	—
99	#13094046	—	2	2	no	—
100	#13094046	—	2	2	no	—
101	#13094046	—	2	2	no	—
102	#13094046	—	2	2	no	—
103	#13094046	—	2	2	no	—
104	#13094046	—	2	2	no	—
105	#13094046	—	2	2	no	—
106	#13094046	—	2	2	no	—
107	#13094046	—	2	4	no	—
108	#13094046	—	2	4	no	—
109	#13094046	—	2	8	no	—
110	#13094046	D₄	1	2	yes	complemented
111	#13094046	D₄	1	2	yes	complemented
112	#13094046	C₂³	1	2	yes	—
113	#13094046	C₂³	1	2	yes	—
114	#13094045	—	2	8	no	—
115	#13094044	—	2	8	no	—
116	#13094043	—	2	4	no	—
117	C₂×Dic₁₈₈	—	2	4	no	—
118	C₂×Dic₁₈₈	D₄	1	1	yes	characteristic, complemented
119	C₂×Dic₁₈₈	C₂³	1	2	yes	—
120	C₂×Dic₁₈₈	C₂³	1	2	yes	—
121	Q₁₆×D₄₇	—	2	4	no	—
122	C₂×#10625325	—	2	8	no	—
123	C₂×#10625325	D₄	1	2	yes	complemented
124	C₂×#10625325	C₂³	1	4	yes	—
125	C₂×#10625325	C₂³	1	4	yes	—
126	SD₁₆×D₄₇	—	2	8	no	—
127	C₂×D₃₇₆	—	2	4	no	—
128	C₂×D₃₇₆	D₄	1	1	yes	characteristic, complemented
129	C₂×D₃₇₆	C₂³	1	2	yes	—
130	C₂×D₃₇₆	C₂³	1	2	yes	—
131	D₈×D₄₇	—	2	4	no	—
132	#13094030	—	2	2	no	—
133	#13094030	—	2	2	no	—
134	#13094030	C₂³	1	4	yes	—
135	#13094030	C₂³	1	4	yes	—
136	C₂×#10625329	C₂³	1	2	yes	—
137	C₂×#10625324	—	2	2	no	—
138	C₂×C₈×D₄₇	—	2	2	no	—
139	#13094024	C₂³	1	2	yes	—
140	#13094021	C₂³	1	2	yes	—
141	#13094012	C₂³	1	4	yes	—
142	#13093998	—	4	2	no	—
143	C₄×D₁₈₈	—	4	2	no	—
144	#13093960	C₂³	1	2	yes	—
145	#13093960	C₂³	1	2	yes	—
146	#13093952	C₂³	1	4	yes	—
147	#13093952	C₂³	1	4	yes	—
148	#13093942	C₂³	1	8	yes	—
149	#13093940	C₂³	1	8	yes	—
150	C₂×#41×C₄₇	C₂³	1	2	yes	—
151	#135×C₄₇	D₄	1	2	yes	complemented
152	#135×C₄₇	D₄	1	2	yes	complemented
153	#135×C₄₇	C₂³	1	2	yes	—
154	#135×C₄₇	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
156	C₂×SD₁₆×C₄₇	D₄	1	2	yes	complemented
157	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic, complemented
158	#131×C₄₇	—	2	2	no	—
159	#131×C₄₇	—	2	2	no	—
160	#131×C₄₇	C₂³	1	4	yes	—
161	#131×C₄₇	C₂³	1	4	yes	—
162	C₂×M₁₆×C₄₇	—	2	2	no	—
163	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
164	C₂²×C₈×C₄₇	—	2	2	no	—
165	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
168	#108×C₄₇	C₂³	1	2	yes	—
169	#108×C₄₇	C₂³	1	2	yes	—
170	#104×C₄₇	C₂³	1	4	yes	—
171	#104×C₄₇	C₂³	1	4	yes	—
172	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
173	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
174	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
176	#41×C₄₇	—	2	2	no	—
177	#41×C₄₇	—	2	2	no	—
178	#41×C₄₇	C₂×D₄	1	4	yes	—
179	#41×C₄₇	C₂⁴	1	4	yes	—
180	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
181	C₂×D₄×C₄₇	—	2	2	no	—
182	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₄₇	—	2	2	no	—
184	C₂²×C₄×C₄₇	—	2	1	no	—
185	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₂×C₂²⋊D₄₇	—	2	2	no	—
187	C₂×C₂²⋊D₄₇	—	2	4	no	—
188	C₂×C₂²⋊D₄₇	—	4	8	no	—
189	#10625354	—	2	8	no	—
190	#10625354	—	4	4	no	—
191	Q₈×D₄₇	—	2	8	no	—
192	Q₈×D₄₇	—	4	4	no	—
193	#10625352	—	2	8	no	—
194	#10625352	—	4	4	no	—
195	#10625352	—	4	8	no	—
196	#10625352	—	4	8	no	—
197	D₄×D₄₇	—	2	8	no	—
198	D₄×D₄₇	—	4	4	no	—
199	D₄×D₄₇	—	4	8	no	—
200	D₄×D₄₇	—	4	8	no	—
201	#10625350	—	2	2	no	—
202	#10625350	—	2	2	no	—
203	#10625350	—	2	4	no	—
204	#10625350	—	2	4	no	—
205	#10625350	—	2	4	no	—
206	#10625350	—	2	4	no	—
207	#10625350	—	2	8	no	—
208	#10625350	—	2	8	no	—
209	#10625350	—	4	8	no	—
210	#10625350	—	4	8	no	—
211	#10625350	C₂×D₄	1	4	yes	—
212	#10625350	C₂⁴	1	4	yes	—
213	C₂×D₁₈₈	—	2	8	no	—
214	C₂×D₁₈₈	—	4	2	no	—
215	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
216	C₂×D₁₈₈	C₂⁴	1	4	yes	—
217	C₂×C₄×D₄₇	—	2	2	no	—
218	C₂×C₄×D₄₇	—	2	4	no	—
219	C₂×C₄×D₄₇	—	4	8	no	—
220	C₂×Dic₉₄	—	2	8	no	—
221	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
222	C₂×Dic₉₄	C₂⁴	1	4	yes	—
223	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
224	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
225	SD₁₆×C₄₇	C₂×D₄	1	4	yes	—
226	SD₁₆×C₄₇	C₂×D₄	1	4	yes	—
227	D₈×C₄₇	C₂×D₄	1	2	yes	—
228	D₈×C₄₇	C₂×D₄	1	2	yes	—
229	M₁₆×C₄₇	—	2	2	no	—
230	M₁₆×C₄₇	—	2	4	no	—
231	M₁₆×C₄₇	—	2	4	no	—
232	M₁₆×C₄₇	C₂⁴	1	4	yes	—
233	C₂×C₈×C₄₇	—	2	2	no	—
234	C₂×C₈×C₄₇	—	2	4	no	—
235	C₂×C₈×C₄₇	—	2	4	no	—
236	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
237	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
238	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
239	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
240	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
241	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
242	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
243	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
244	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₄²×C₄₇	—	2	1	no	—
249	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
251	#10625337	—	2	8	no	—
252	#10625336	—	2	8	no	—
253	#10625335	—	2	8	no	—
254	#10625334	—	2	8	no	—
255	(C₂×D₄₇)⋊C₄	—	4	4	no	—
256	C₄⋊Dic₄₇	—	4	2	no	—
257	#10625329	—	2	2	no	—
258	#10625329	C₂⁴	1	4	yes	—
259	C₂×C₄₇⋊C₈	—	2	2	no	—
260	Dic₁₈₈	—	2	8	no	—
261	Dic₁₈₈	—	2	2	no	—
262	Dic₁₈₈	—	2	2	no	—
263	Dic₁₈₈	—	2	2	no	—
264	Dic₁₈₈	—	2	2	no	—
265	Dic₁₈₈	C₂×D₄	1	2	yes	—
266	Dic₁₈₈	C₂×D₄	1	2	yes	—
267	D₃₇₆	—	2	8	no	—
268	D₃₇₆	—	2	2	no	—
269	D₃₇₆	—	2	2	no	—
270	D₃₇₆	—	2	2	no	—
271	D₃₇₆	—	2	2	no	—
272	D₃₇₆	C₂×D₄	1	2	yes	—
273	D₃₇₆	C₂×D₄	1	2	yes	—
274	#10625325	—	2	8	no	—
275	#10625325	—	2	8	no	—
276	#10625325	—	2	4	no	—
277	#10625325	—	2	4	no	—
278	#10625325	—	2	4	no	—
279	#10625325	—	2	4	no	—
280	#10625325	C₂×D₄	1	4	yes	—
281	#10625325	C₂×D₄	1	4	yes	—
282	#10625324	—	2	4	no	—
283	#10625324	—	2	4	no	—
284	C₈×D₄₇	—	2	4	no	—
285	C₈×D₄₇	—	2	4	no	—
286	C₂³×C₄₇	—	2	2	no	—
287	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×D₄₇	—	2	2	no	—
289	C₂²×D₄₇	—	2	4	no	—
290	C₂²×D₄₇	—	4	8	no	—
291	Q₈×C₄₇	—	2	2	no	—
292	Q₈×C₄₇	C₂²×D₄	1	4	yes	—
293	D₄×C₄₇	—	2	4	no	—
294	D₄×C₄₇	—	2	4	no	—
295	D₄×C₄₇	—	2	2	no	—
296	D₄×C₄₇	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₄₇	—	2	2	no	—
298	C₂×C₄×C₄₇	—	2	1	no	—
299	C₂×C₄×C₄₇	—	2	4	no	—
300	C₂×C₄×C₄₇	—	2	4	no	—
301	C₂×C₄×C₄₇	—	2	1	no	—
302	C₂×C₄×C₄₇	—	4	2	no	—
303	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
309	C₂²⋊D₄₇	—	2	4	no	—
310	C₂²⋊D₄₇	—	2	4	no	—
311	C₂²⋊D₄₇	—	4	8	no	—
312	C₂²⋊D₄₇	—	4	8	no	—
313	C₂²⋊D₄₇	—	4	4	no	—
314	C₂²⋊D₄₇	—	4	4	no	—
315	C₂×Dic₄₇	—	2	2	no	—
316	C₂×Dic₄₇	—	2	4	no	—
317	C₂×Dic₄₇	—	4	8	no	—
318	D₁₈₈	—	2	2	no	—
319	D₁₈₈	—	2	4	no	—
320	D₁₈₈	—	2	4	no	—
321	D₁₈₈	—	4	8	no	—
322	D₁₈₈	—	8	4	no	—
323	D₁₈₈	C₂²×D₄	1	4	yes	—
324	C₄×D₄₇	—	2	4	no	—
325	C₄×D₄₇	—	2	4	no	—
326	C₄×D₄₇	—	4	8	no	—
327	C₄×D₄₇	—	4	8	no	—
328	C₄×D₄₇	—	4	4	no	—
329	C₄×D₄₇	—	4	4	no	—
330	Dic₉₄	—	2	2	no	—
331	Dic₉₄	—	2	4	no	—
332	Dic₉₄	—	2	4	no	—
333	Dic₉₄	—	4	8	no	—
334	Dic₉₄	C₂²×D₄	1	4	yes	—
335	C₈×C₄₇	—	2	4	no	—
336	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
337	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
338	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
339	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
340	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
341	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
342	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
343	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
344	C₄₇⋊C₈	—	2	4	no	—
345	#61105	—	47	1	no	maximal, Sylow
346	C₂²×C₄₇	—	2	4	no	—
347	C₂²×C₄₇	—	4	1	no	—
348	C₂²×C₄₇	—	8	2	no	—
349	C₂²×C₄₇	D₄²	1	1	yes	characteristic
350	C₂²×C₄₇	D₄²	1	1	yes	characteristic
351	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×D₄₇	—	2	4	no	—
353	C₂×D₄₇	—	4	4	no	—
354	C₂×D₄₇	—	8	2	no	—
355	C₂×D₄₇	—	8	4	no	—
356	C₂×D₄₇	—	16	8	no	—
357	C₄×C₄₇	—	2	2	no	—
358	C₄×C₄₇	—	2	4	no	—
359	C₄×C₄₇	—	4	1	no	—
360	C₄×C₄₇	D₄²	1	1	yes	characteristic
361	C₄×C₄₇	D₄²	1	1	yes	characteristic
362	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
364	Dic₄₇	—	2	4	no	—
365	Dic₄₇	—	4	4	no	—
366	#3584	—	47	2	no	—
367	#3584	—	47	2	no	—
368	#3293	—	47	2	no	—
369	#3292	—	47	2	no	—
370	#3291	—	47	4	no	—
371	#3290	—	47	4	no	—
372	#3290	—	47	4	no	—
373	#3147	—	47	1	no	—
374	#3067	—	47	2	no	—
375	#3067	—	47	2	no	—
376	#3018	—	47	4	no	—
377	C₂×#443	—	47	1	no	—
378	C₂×#443	D₄₇	1	1	yes	characteristic, complemented
379	C₂×C₄₇	—	2	1	no	—
380	C₂×C₄₇	—	2	1	no	—
381	C₂×C₄₇	—	2	1	no	—
382	C₂×C₄₇	—	4	4	no	—
383	C₂×C₄₇	C₂×D₄²	1	1	yes	characteristic
384	D₄₇	—	4	4	no	—
385	D₄₇	—	8	4	no	—
386	#585	—	47	4	no	—
387	#578	—	47	4	no	—
388	#578	—	47	4	no	—
389	#578	—	94	2	no	—
390	#578	—	94	2	no	—
391	#577	—	47	8	no	—
392	#577	—	47	8	no	—
393	#577	—	94	4	no	—
394	#577	—	94	4	no	—
395	#576	—	47	4	no	—
396	#576	—	47	4	no	—
397	#576	—	94	2	no	—
398	#576	—	94	2	no	—
399	#575	—	47	4	no	—
400	#575	—	47	4	no	—
401	#575	—	94	4	no	—
402	#575	—	94	4	no	—
403	C₂×#135	—	47	1	no	—
404	C₂×#135	—	47	2	no	—
405	C₂×#135	—	47	2	no	—
406	C₂×#135	—	94	4	no	—
407	C₂×#135	—	94	4	no	—
408	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
409	C₂×#131	—	47	2	no	—
410	C₂×#131	C₂×D₄₇	1	2	yes	complemented
411	#532	—	47	2	no	—
412	#495	—	47	2	no	—
413	#495	—	47	2	no	—
414	#494	—	47	1	no	—
415	#493	—	47	1	no	—
416	#492	—	47	2	no	—
417	#473	—	47	4	no	—
418	#473	—	47	4	no	—
419	#472	—	47	4	no	—
420	#472	—	47	4	no	—
421	#471	—	47	8	no	—
422	#471	—	47	8	no	—
423	#456	—	47	8	no	—
424	#455	—	47	8	no	—
425	#454	—	47	8	no	—
426	#453	—	47	8	no	—
427	#443	—	47	2	no	—
428	#443	—	47	2	no	—
429	#443	—	47	2	no	—
430	#443	—	47	2	no	—
431	#443	C₂×D₄₇	1	2	yes	complemented
432	#443	C₂×D₄₇	1	2	yes	complemented
433	#443	C₂×D₄₇	1	2	yes	complemented
434	#443	C₂×D₄₇	1	2	yes	complemented
435	C₂×#108	—	47	1	no	—
436	C₂×#108	C₂×D₄₇	1	1	yes	characteristic, complemented
437	C₂×#104	—	47	2	no	—
438	C₂×#104	C₂×D₄₇	1	2	yes	complemented
439	#413	—	47	4	no	—
440	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
441	C₄₇	#61105	1	1	yes	characteristic, complemented, Sylow
442	2₋¹⁺⁴	—	47	8	no	—
443	2₋¹⁺⁴	—	94	4	no	—
444	2₋¹⁺⁴	—	94	4	no	—
445	H(5,𝔽₂)	—	47	8	no	—
446	H(5,𝔽₂)	—	94	4	no	—
447	H(5,𝔽₂)	—	94	4	no	—
448	H(5,𝔽₂)	—	188	4	no	—
449	C₂×#41	—	47	2	no	—
450	C₂×#41	—	47	4	no	—
451	C₂×#41	—	94	8	no	—
452	C₂×#41	—	94	8	no	—
453	C₂×#41	—	188	4	no	—
454	C₂×#41	C₂²×D₄₇	1	2	yes	—
455	#137	—	47	8	no	—
456	#137	—	47	8	no	—
457	#137	—	94	8	no	—
458	#137	—	94	8	no	—
459	#137	—	94	4	no	—
460	#137	—	94	4	no	—
461	#137	—	94	8	no	—
462	#137	—	94	8	no	—
463	AGL(1,ℤ/8)	—	47	8	no	—
464	AGL(1,ℤ/8)	—	47	8	no	—
465	AGL(1,ℤ/8)	—	94	8	no	—
466	AGL(1,ℤ/8)	—	94	8	no	—
467	AGL(1,ℤ/8)	—	94	4	no	—
468	AGL(1,ℤ/8)	—	94	4	no	—
469	AGL(1,ℤ/8)	—	94	8	no	—
470	AGL(1,ℤ/8)	—	94	8	no	—
471	#135	—	47	2	no	—
472	#135	—	47	2	no	—
473	#135	—	47	2	no	—
474	#135	—	47	2	no	—
475	#135	—	94	4	no	—
476	#135	—	94	8	no	—
477	#135	—	94	4	no	—
478	#135	—	94	8	no	—
479	#135	—	94	8	no	—
480	#135	—	94	4	no	—
481	#135	—	94	8	no	—
482	#135	—	94	4	no	—
483	#135	—	94	2	no	—
484	#135	—	94	2	no	—
485	#135	—	94	2	no	—
486	#135	—	94	2	no	—
487	#135	—	94	2	no	—
488	#135	—	94	2	no	—
489	#135	—	94	2	no	—
490	#135	—	94	2	no	—
491	#135	D₁₈₈	1	2	yes	complemented
492	#135	D₁₈₈	1	2	yes	complemented
493	#135	C₂²×D₄₇	1	2	yes	—
494	#135	C₂²×D₄₇	1	2	yes	—
495	C₂×Q₁₆	—	47	1	no	—
496	C₂×Q₁₆	—	47	2	no	—
497	C₂×Q₁₆	—	47	2	no	—
498	C₂×Q₁₆	—	94	4	no	—
499	C₂×Q₁₆	—	94	4	no	—
500	C₂×Q₁₆	D₁₈₈	1	1	yes	characteristic, complemented
501	C₂×SD₁₆	—	47	2	no	—
502	C₂×SD₁₆	—	47	4	no	—
503	C₂×SD₁₆	—	47	4	no	—
504	C₂×SD₁₆	—	94	8	no	—
505	C₂×SD₁₆	—	94	8	no	—
506	C₂×SD₁₆	D₁₈₈	1	2	yes	complemented
507	C₂×D₈	—	47	1	no	—
508	C₂×D₈	—	47	2	no	—
509	C₂×D₈	—	47	2	no	—
510	C₂×D₈	—	94	4	no	—
511	C₂×D₈	—	94	4	no	—
512	C₂×D₈	D₁₈₈	1	1	yes	characteristic, complemented
513	#131	—	2	2	no	—
514	#131	—	2	2	no	—
515	#131	—	47	4	no	—
516	#131	—	47	4	no	—
517	#131	—	94	2	no	—
518	#131	—	94	2	no	—
519	#131	C₂²×D₄₇	1	4	yes	—
520	#131	C₂²×D₄₇	1	4	yes	—
521	C₂×M₁₆	—	2	2	no	—
522	C₂×M₁₆	—	47	2	no	—
523	C₂×M₁₆	—	94	2	no	—
524	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
525	C₂²×C₈	—	2	2	no	—
526	C₂²×C₈	—	94	2	no	—
527	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
528	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
529	C₄⋊Q₈	—	47	2	no	—
530	#127	—	47	2	no	—
531	#124	—	47	4	no	—
532	#121	—	188	2	no	—
533	C₄×D₄	—	188	2	no	—
534	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
535	#108	—	47	2	no	—
536	#108	—	47	2	no	—
537	#108	C₂²×D₄₇	1	2	yes	—
538	#108	C₂²×D₄₇	1	2	yes	—
539	#104	—	47	4	no	—
540	#104	—	47	4	no	—
541	#104	C₂²×D₄₇	1	4	yes	—
542	#104	C₂²×D₄₇	1	4	yes	—
543	#101	—	47	8	no	—
544	#100	—	47	8	no	—
545	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
546	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
547	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
548	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
549	#41	—	2	2	no	—
550	#41	—	2	2	no	—
551	#41	—	47	4	no	—
552	#41	—	47	4	no	—
553	#41	—	94	8	no	—
554	#41	—	94	8	no	—
555	#41	—	94	2	no	—
556	#41	—	94	2	no	—
557	#41	—	94	8	no	—
558	#41	—	94	8	no	—
559	#41	—	94	4	no	—
560	#41	—	94	4	no	—
561	#41	—	94	4	no	—
562	#41	—	94	4	no	—
563	#41	—	188	8	no	—
564	#41	—	188	8	no	—
565	#41	—	188	8	no	—
566	#41	—	188	8	no	—
567	#41	—	188	4	no	—
568	#41	—	188	4	no	—
569	#41	C₂×D₁₈₈	1	4	yes	—
570	#41	C₂³×D₄₇	1	4	yes	—
571	C₂×Q₈	—	47	2	no	—
572	C₂×Q₈	—	47	4	no	—
573	C₂×Q₈	—	94	8	no	—
574	C₂×Q₈	—	94	8	no	—
575	C₂×Q₈	—	188	4	no	—
576	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	47	2	no	—
579	C₂×D₄	—	47	4	no	—
580	C₂×D₄	—	94	8	no	—
581	C₂×D₄	—	94	2	no	—
582	C₂×D₄	—	94	8	no	—
583	C₂×D₄	—	94	4	no	—
584	C₂×D₄	—	188	2	no	—
585	C₂×D₄	—	188	8	no	—
586	C₂×D₄	—	188	4	no	—
587	C₂×D₄	—	188	8	no	—
588	C₂×D₄	—	188	8	no	—
589	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	94	2	no	—
593	C₂²×C₄	—	94	4	no	—
594	C₂²×C₄	—	188	8	no	—
595	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
596	Q₁₆	—	47	2	no	—
597	Q₁₆	—	47	2	no	—
598	Q₁₆	—	94	8	no	—
599	Q₁₆	—	94	8	no	—
600	Q₁₆	—	94	2	no	—
601	Q₁₆	—	94	2	no	—
602	Q₁₆	—	94	2	no	—
603	Q₁₆	—	94	2	no	—
604	Q₁₆	C₂×D₁₈₈	1	2	yes	—
605	Q₁₆	C₂×D₁₈₈	1	2	yes	—
606	SD₁₆	—	47	4	no	—
607	SD₁₆	—	47	4	no	—
608	SD₁₆	—	94	8	no	—
609	SD₁₆	—	94	8	no	—
610	SD₁₆	—	94	8	no	—
611	SD₁₆	—	94	8	no	—
612	SD₁₆	—	94	4	no	—
613	SD₁₆	—	94	4	no	—
614	SD₁₆	—	94	4	no	—
615	SD₁₆	—	94	4	no	—
616	SD₁₆	C₂×D₁₈₈	1	4	yes	—
617	SD₁₆	C₂×D₁₈₈	1	4	yes	—
618	D₈	—	47	2	no	—
619	D₈	—	47	2	no	—
620	D₈	—	94	8	no	—
621	D₈	—	94	8	no	—
622	D₈	—	94	2	no	—
623	D₈	—	94	2	no	—
624	D₈	—	94	2	no	—
625	D₈	—	94	2	no	—
626	D₈	C₂×D₁₈₈	1	2	yes	—
627	D₈	C₂×D₁₈₈	1	2	yes	—
628	M₁₆	—	2	2	no	—
629	M₁₆	—	2	4	no	—
630	M₁₆	—	2	4	no	—
631	M₁₆	—	47	4	no	—
632	M₁₆	—	94	2	no	—
633	M₁₆	—	94	4	no	—
634	M₁₆	—	94	4	no	—
635	M₁₆	C₂³×D₄₇	1	4	yes	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	2	4	no	—
639	C₂×C₈	—	94	2	no	—
640	C₂×C₈	—	94	4	no	—
641	C₂×C₈	—	94	4	no	—
642	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
643	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
644	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
645	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
646	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
647	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
648	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
649	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
650	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
651	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
652	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
653	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
654	C₄⋊C₄	—	188	2	no	—
655	C₂²⋊C₄	—	188	4	no	—
656	C₄²	—	2	1	no	—
657	C₄²	C₂³×D₄₇	1	1	yes	characteristic
658	C₄²	C₂³×D₄₇	1	1	yes	characteristic
659	C₂³	—	2	2	no	—
660	C₂³	—	94	2	no	—
661	C₂³	—	94	4	no	—
662	C₂³	—	188	8	no	—
663	C₂³	#13094070	1	1	yes	characteristic
664	Q₈	—	2	2	no	—
665	Q₈	—	47	4	no	—
666	Q₈	—	94	2	no	—
667	Q₈	—	94	4	no	—
668	Q₈	—	94	4	no	—
669	Q₈	—	188	8	no	—
670	Q₈	C₂²×D₁₈₈	1	4	yes	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	2	no	—
674	D₄	—	47	4	no	—
675	D₄	—	94	4	no	—
676	D₄	—	94	4	no	—
677	D₄	—	94	2	no	—
678	D₄	—	94	4	no	—
679	D₄	—	94	4	no	—
680	D₄	—	376	4	no	—
681	D₄	—	188	8	no	—
682	D₄	—	188	8	no	—
683	D₄	—	188	8	no	—
684	D₄	—	188	4	no	—
685	D₄	—	188	4	no	—
686	D₄	C₂²×D₁₈₈	1	4	yes	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	94	2	no	—
694	C₂×C₄	—	94	4	no	—
695	C₂×C₄	—	94	4	no	—
696	C₂×C₄	—	94	4	no	—
697	C₂×C₄	—	188	8	no	—
698	C₂×C₄	—	188	8	no	—
699	C₂×C₄	—	188	8	no	—
700	C₂×C₄	—	188	4	no	—
701	C₂×C₄	—	188	4	no	—
702	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
703	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
706	C₂×C₄	#13094070	1	1	yes	characteristic
707	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
708	C₈	—	2	4	no	—
709	C₈	—	94	4	no	—
710	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
711	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
712	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
713	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
714	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
715	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
716	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
717	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
718	C₂²	—	2	4	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	8	2	no	—
721	C₂²	—	94	4	no	—
722	C₂²	—	376	4	no	—
723	C₂²	—	376	2	no	—
724	C₂²	—	188	4	no	—
725	C₂²	—	752	8	no	—
726	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
727	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
728	C₂²	C₂×#13094070	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	4	1	no	—
732	C₄	—	94	4	no	—
733	C₄	—	188	4	no	—
734	C₄	D₄×D₁₈₈	1	1	yes	characteristic
735	C₄	D₄×D₁₈₈	1	1	yes	characteristic
736	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
737	C₄	C₂³×D₁₈₈	1	1	yes	characteristic
738	C₂	—	2	1	no	—
739	C₂	—	2	1	no	—
740	C₂	—	2	1	no	—
741	C₂	—	4	4	no	—
742	C₂	—	376	4	no	—
743	C₂	—	188	4	no	—
744	C₂	C₂×D₄×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#443	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	#61105
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #20258162	C₂	semidirect
2. #20258157	C₂	semidirect
3. #20255193	C₂	semidirect
4. #20255188	C₂	semidirect
5. #20255182	C₂	semidirect
6. #20255176	C₂	semidirect
7. #20255175	C₂	semidirect
8. #20253816	C₂	semidirect
9. #20253109	C₂	semidirect
10. #20253108	C₂	semidirect
11. #20252739	C₂	semidirect
12. C₂×#15689241	C₂	semidirect
13. C₂×C₄₇×#443	C₂	semidirect
14. #15689959	C₂²	semidirect
16. #15689940	C₂²	semidirect
17. #15689937	C₂²	semidirect
20. #15689935	C₂²	semidirect
21. #15689930	C₂²	semidirect
24. #15689928	C₂²	semidirect
25. #15689925	C₂²	semidirect
28. #15689923	C₂²	semidirect
29. #15689921	C₂²	semidirect
33. C₂×#13094046	C₂²	semidirect
34. C₂×#13094046	C₂²	semidirect
36. C₂×#13094030	C₂²	semidirect
37. #15689673	C₂²	semidirect
38. #15689507	C₂²	semidirect
39. #15689507	C₂²	semidirect
40. #15689503	C₂²	semidirect
41. #15689500	C₂²	semidirect
42. #15689496	C₂²	semidirect
43. #15689399	C₂²	semidirect
44. #15689398	C₂²	semidirect
45. #15689394	C₂²	semidirect
46. #15689393	C₂²	semidirect
47. #15689387	C₂²	semidirect
48. #15689386	C₂²	semidirect
49. #15689307	C₂²	semidirect
50. #15689302	C₂²	semidirect
51. #15689297	C₂²	semidirect
52. #15689292	C₂²	semidirect
53. #15689241	C₂²	semidirect
54. #15689241	C₂²	semidirect
55. #15689241	C₂²	semidirect
56. #15689241	C₂²	semidirect
57. C₂×#13093960	C₂²	semidirect
58. C₂×#13093952	C₂²	semidirect
59. #15689105	C₂²	semidirect
61. C₂×#131×C₄₇	C₂²	semidirect
62. C₄₇×#443	C₂²	semidirect
63. C₄₇×#443	C₂²	semidirect
64. C₄₇×#443	C₂²	semidirect
65. C₄₇×#443	C₂²	semidirect
66. C₂×#108×C₄₇	C₂²	semidirect
67. C₂×#104×C₄₇	C₂²	semidirect
68. C₂×C₄×C₈×C₄₇	C₂²	semidirect
110. #13094046	D₄	semidirect
111. #13094046	D₄	semidirect
118. C₂×Dic₁₈₈	D₄	semidirect
123. C₂×#10625325	D₄	semidirect
128. C₂×D₃₇₆	D₄	semidirect
151. #135×C₄₇	D₄	semidirect
152. #135×C₄₇	D₄	semidirect
155. C₂×Q₁₆×C₄₇	D₄	semidirect
156. C₂×SD₁₆×C₄₇	D₄	semidirect
157. C₂×D₈×C₄₇	D₄	semidirect
378. C₂×#443	D₄₇	semidirect
410. C₂×#131	C₂×D₄₇	semidirect
431. #443	C₂×D₄₇	semidirect
432. #443	C₂×D₄₇	semidirect
433. #443	C₂×D₄₇	semidirect
434. #443	C₂×D₄₇	semidirect
436. C₂×#108	C₂×D₄₇	semidirect
438. C₂×#104	C₂×D₄₇	semidirect
440. C₂×C₄×C₈	C₂×D₄₇	semidirect
441. C₄₇	#61105	semidirect
491. #135	D₁₈₈	semidirect
492. #135	D₁₈₈	semidirect
500. C₂×Q₁₆	D₁₈₈	semidirect
506. C₂×SD₁₆	D₁₈₈	semidirect
512. C₂×D₈	D₁₈₈	semidirect

Maximal subgroups

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

subgroup	index
#20258162	2
#20258157	2
#20255193	2
#20255188	2
#20255182	2
#20255176	2
#20255175	2
#20253816	2
#20253109	2
#20253108	2
#20252739	2
C₂×#15689241	2
C₂×C₄₇×#443	2
#61105	47