Subgroups — #26234771

Order 12032.

862 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689238	C₂	1	1	yes	maximal, characteristic
2	#20252259	C₂	1	2	yes	maximal
3	#20251988	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251984	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244172	C₂	1	2	yes	maximal, complemented
6	#20243617	C₂	1	2	yes	maximal, complemented
7	#20243612	C₂	1	2	yes	maximal, complemented
8	#20243546	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243449	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	#15689606	C₂²	1	2	yes	—
15	#15689604	C₂²	1	2	yes	—
16	#15689238	C₄	1	8	yes	complemented
17	#15689226	—	2	2	no	—
18	#15689220	—	2	2	no	—
19	#15689215	—	2	2	no	—
20	#15689203	—	2	2	no	—
21	C₂×#13093959	C₂²	1	1	yes	characteristic
22	#15689165	—	2	2	no	—
23	#15689165	C₂²	1	2	yes	—
24	#15689164	—	2	2	no	—
25	#15689163	C₂²	1	2	yes	—
26	#15689161	—	2	1	no	—
27	#15689161	C₂²	1	1	yes	characteristic
28	#15689160	—	2	1	no	—
29	C₂×#13093958	—	2	1	no	—
30	C₂×#13093958	C₂²	1	1	yes	characteristic
31	C₂×#13093957	C₂²	1	2	yes	—
32	#107×D₄₇	—	2	1	no	—
33	C₂×#13093951	C₂²	1	1	yes	characteristic
34	C₂×#13093950	C₂²	1	1	yes	characteristic
35	#15689125	C₂²	1	2	yes	—
36	#15689081	C₂²	1	2	yes	—
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	#15688992	C₂²	1	2	yes	—
39	#15688891	C₂²	1	2	yes	—
40	#15688884	C₂²	1	2	yes	—
41	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#417	C₂²	1	2	yes	—
45	C₄₇×#343	C₂²	1	2	yes	—
46	C₂×#10625350	C₂³	1	1	yes	characteristic
47	#13094044	C₂×C₄	1	4	yes	—
48	#13094044	Q₈	1	4	yes	—
49	C₂×#10625337	D₄	1	1	yes	characteristic
50	C₂×#10625335	D₄	1	1	yes	characteristic
51	C₂×#10625336	D₄	1	1	yes	characteristic
52	C₂×#10625334	D₄	1	1	yes	characteristic
53	#13094030	—	2	2	no	—
54	#13094030	C₂×C₄	1	4	yes	complemented
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×#10625324	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₇	—	2	1	no	—
59	Q₈×Dic₄₇	—	2	2	no	—
60	#13093989	—	2	2	no	—
61	D₄×Dic₄₇	—	2	2	no	—
62	D₄×Dic₄₇	—	4	2	no	—
63	#13093986	—	2	2	no	—
64	C₄×C₂²⋊D₄₇	—	4	2	no	—
65	#13093983	—	2	2	no	—
66	#13093983	C₂³	1	2	yes	—
67	#13093982	—	2	2	no	—
68	C₂×C₄⋊Dic₄₇	—	2	2	no	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×Dic₄₇⋊C₄	—	4	2	no	—
71	C₄⋊C₄×D₄₇	—	2	2	no	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	#13093959	C₂×C₄	1	4	yes	complemented
74	#13093958	—	2	1	no	—
75	#13093958	—	2	1	no	—
76	#13093958	—	2	2	no	—
77	#13093958	D₄	1	1	yes	characteristic
78	#13093958	D₄	1	1	yes	characteristic
79	#13093957	—	2	2	no	—
80	#13093957	—	2	2	no	—
81	#13093957	—	2	2	no	—
82	#13093956	—	2	2	no	—
83	#13093956	D₄	1	2	yes	—
84	#13093955	—	2	2	no	—
85	#13093951	C₂×C₄	1	4	yes	complemented
86	#13093950	C₂×C₄	1	4	yes	complemented
87	#13093949	—	2	2	no	—
88	#13093946	—	2	2	no	—
89	#13093934	—	2	2	no	—
90	C₈×Dic₄₇	—	2	2	no	—
91	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
92	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
93	#131×C₄₇	—	2	2	no	—
94	#131×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
97	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	—	2	1	no	—
99	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
101	#108×C₄₇	—	2	2	no	—
102	#107×C₄₇	—	2	1	no	—
103	#107×C₄₇	—	2	1	no	—
104	#103×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	2	no	—
106	#41×C₄₇	—	2	1	no	—
107	#41×C₄₇	—	2	1	no	—
108	#41×C₄₇	C₂²×C₄	1	2	yes	—
109	#41×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₇	—	2	1	no	—
117	C₂²×Dic₄₇	—	2	1	no	—
118	C₂²×Dic₄₇	—	2	2	no	—
119	C₂²×Dic₄₇	—	4	2	no	—
120	#10625350	—	2	1	no	—
121	#10625350	—	2	1	no	—
122	#10625350	C₂²×C₄	1	2	yes	—
123	#10625350	C₂×Q₈	1	2	yes	—
124	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	1	no	—
126	C₂×C₄×D₄₇	—	4	2	no	—
127	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
128	M₁₆×C₄₇	—	2	1	no	—
129	M₁₆×C₄₇	—	2	4	no	—
130	M₁₆×C₄₇	—	2	2	no	—
131	M₁₆×C₄₇	—	2	2	no	—
132	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	4	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	#41	1	2	yes	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₂²⋊Dic₄₇	—	2	2	no	—
143	C₂²⋊Dic₄₇	—	4	2	no	—
144	#10625337	C₄⋊C₄	1	4	yes	complemented
145	#10625336	C₄⋊C₄	1	4	yes	complemented
146	#10625335	C₄⋊C₄	1	4	yes	complemented
147	#10625334	C₄⋊C₄	1	4	yes	complemented
148	(C₂×D₄₇)⋊C₄	—	4	2	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	4	2	no	—
152	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
153	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
154	Dic₄₇⋊C₄	—	4	2	no	—
155	Dic₄₇⋊C₄	—	8	4	no	—
156	C₄×Dic₄₇	—	2	2	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	C₄×Dic₄₇	—	4	2	no	—
159	C₄×Dic₄₇	—	4	2	no	—
160	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
161	#10625329	—	2	1	no	—
162	#10625329	C₂²×C₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	—	2	1	no	—
164	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
168	#10625324	—	2	4	no	—
169	C₈×D₄₇	—	2	4	no	—
170	C₂³×C₄₇	—	2	1	no	—
171	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×D₄₇	—	2	1	no	—
173	Q₈×C₄₇	—	2	1	no	—
174	Q₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
175	D₄×C₄₇	—	2	2	no	—
176	D₄×C₄₇	—	2	2	no	—
177	D₄×C₄₇	—	2	1	no	—
178	D₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	8	2	no	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂²⋊D₄₇	—	2	2	no	—
191	C₂²⋊D₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	2	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	8	2	no	—
200	C₂×Dic₄₇	—	16	2	no	—
201	D₁₈₈	—	2	1	no	—
202	D₁₈₈	C₂×C₄⋊C₄	1	2	yes	—
203	C₄×D₄₇	—	2	2	no	—
204	C₄×D₄₇	—	2	2	no	—
205	C₄×D₄₇	—	16	2	no	—
206	Dic₉₄	—	2	1	no	—
207	Dic₉₄	C₂×C₄⋊C₄	1	2	yes	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	4	2	no	—
210	C₈×C₄₇	C₄×D₄	1	2	yes	—
211	C₈×C₄₇	C₄×D₄	1	2	yes	—
212	C₄₇⋊C₈	—	2	2	no	—
213	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
214	C₄₇⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
215	#22692	—	47	1	no	maximal, Sylow
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	4	1	no	—
220	C₂²×C₄₇	—	4	1	no	—
221	C₂²×C₄₇	#520	1	1	yes	characteristic
222	C₂²×C₄₇	D₄²	1	1	yes	characteristic
223	C₂²×C₄₇	#554	1	1	yes	characteristic
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	4	1	no	—
226	C₂×D₄₇	—	4	1	no	—
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	8	2	no	—
229	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
230	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₄₇	#547	1	1	yes	characteristic
232	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
233	Dic₄₇	—	2	4	no	—
234	Dic₄₇	—	2	2	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	—	4	2	no	—
237	Dic₄₇	—	8	2	no	—
238	C₂×#443	—	47	1	no	—
239	#2951	—	47	2	no	—
240	#2913	—	47	1	no	—
241	#2913	—	47	1	no	—
242	#1952	—	47	2	no	—
243	#1859	—	47	2	no	—
244	#1859	—	47	2	no	—
245	#1845	—	47	1	no	—
246	#1816	—	47	1	no	—
247	#1816	D₄₇	1	1	yes	characteristic, complemented
248	#1772	—	47	1	no	—
249	C₂×C₄₇	—	2	1	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	4	2	no	—
252	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₄₇	#3292	1	1	yes	characteristic
254	C₂×C₄₇	#3293	1	1	yes	characteristic
255	D₄₇	—	4	2	no	—
256	C₂×#135	—	47	1	no	—
257	C₂×#131	—	47	1	no	—
258	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
259	#520	—	47	2	no	—
260	#520	—	47	2	no	—
261	#443	—	47	8	no	—
262	#440	—	94	2	no	—
263	#440	—	94	2	no	—
264	C₄×Q₁₆	—	94	2	no	—
265	C₄×D₈	—	94	2	no	—
266	C₂×#108	—	47	1	no	—
267	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
268	#428	—	47	2	no	—
269	#428	—	47	2	no	—
270	#428	—	94	2	no	—
271	#428	—	94	2	no	—
272	#427	—	47	1	no	—
273	#427	—	94	1	no	—
274	#427	—	94	1	no	—
275	C₂×#107	—	47	1	no	—
276	C₂×#107	—	47	2	no	—
277	C₂×#107	—	94	1	no	—
278	C₂×#107	—	94	1	no	—
279	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
280	C₂×#104	—	47	1	no	—
281	C₂×#104	—	47	1	no	—
282	#417	—	47	2	no	—
283	#417	C₂×D₄₇	1	2	yes	—
284	#405	—	47	2	no	—
285	C₂×C₄×C₈	—	47	1	no	—
286	#384	—	47	2	no	—
287	#343	—	47	2	no	—
288	#343	C₂×D₄₇	1	2	yes	—
289	#339	—	47	2	no	—
290	C₄₇	#22692	1	1	yes	characteristic, complemented, Sylow
291	C₂×#41	—	47	1	no	—
292	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
293	#135	—	47	4	no	—
294	#135	—	47	4	no	—
295	C₂×Q₁₆	—	47	1	no	—
296	C₂×SD₁₆	—	47	1	no	—
297	C₂×SD₁₆	—	47	1	no	—
298	C₂×D₈	—	47	1	no	—
299	#131	—	2	2	no	—
300	#131	—	47	4	no	—
301	#131	—	94	2	no	—
302	#131	C₄×D₄₇	1	4	yes	complemented
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	47	1	no	—
305	C₂×M₁₆	—	94	1	no	—
306	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
307	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	47	1	no	—
310	C₂²×C₈	—	94	1	no	—
311	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄×Q₈	—	94	2	no	—
313	C₄×Q₈	—	94	2	no	—
314	C₄×D₄	—	94	2	no	—
315	C₄×D₄	—	94	2	no	—
316	C₄×D₄	—	188	2	no	—
317	C₄×D₄	—	188	2	no	—
318	#117	—	47	2	no	—
319	#117	—	94	2	no	—
320	#117	—	94	2	no	—
321	C₂×C₄⋊C₄	—	47	2	no	—
322	C₂×C₄⋊C₄	—	94	2	no	—
323	C₂×C₄⋊C₄	—	94	2	no	—
324	C₂×C₄⋊C₄	—	188	2	no	—
325	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
326	C₂×C₄²	—	47	1	no	—
327	#108	—	2	2	no	—
328	#108	—	47	4	no	—
329	#107	—	2	1	no	—
330	#107	—	2	1	no	—
331	#107	—	47	1	no	—
332	#107	—	47	1	no	—
333	#107	—	94	2	no	—
334	#107	—	94	2	no	—
335	#107	—	94	2	no	—
336	#107	—	94	2	no	—
337	#107	—	94	1	no	—
338	#107	—	94	1	no	—
339	#106	—	47	2	no	—
340	#106	—	94	2	no	—
341	#106	—	94	2	no	—
342	#104	—	47	4	no	—
343	#104	—	47	4	no	—
344	#103	—	2	2	no	—
345	#103	—	94	2	no	—
346	#102	—	2	2	no	—
347	#102	—	94	2	no	—
348	#97	—	94	2	no	—
349	C₄×C₈	—	47	4	no	—
350	C₄×C₈	—	94	2	no	—
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	—	47	2	no	—
354	#41	—	47	2	no	—
355	#41	—	94	1	no	—
356	#41	—	94	1	no	—
357	#41	C₂×C₄×D₄₇	1	2	yes	—
358	#41	Q₈×D₄₇	1	2	yes	—
359	C₂×Q₈	—	47	1	no	—
360	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	47	1	no	—
363	C₂×D₄	—	94	1	no	—
364	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	2	no	—
370	C₂²×C₄	—	188	2	no	—
371	C₂²×C₄	—	188	2	no	—
372	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
373	Q₁₆	—	47	4	no	—
374	SD₁₆	—	47	4	no	—
375	SD₁₆	—	47	4	no	—
376	D₈	—	47	4	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	47	2	no	—
382	M₁₆	—	94	1	no	—
383	M₁₆	—	94	4	no	—
384	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	47	2	no	—
389	C₂×C₈	—	47	1	no	—
390	C₂×C₈	—	47	1	no	—
391	C₂×C₈	—	47	2	no	—
392	C₂×C₈	—	94	1	no	—
393	C₂×C₈	—	94	4	no	—
394	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
395	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
396	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
397	C₂×C₈	#10625352	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	47	2	no	—
401	C₄⋊C₄	—	47	2	no	—
402	C₄⋊C₄	—	94	2	no	—
403	C₄⋊C₄	—	94	2	no	—
404	C₄⋊C₄	—	376	4	no	—
405	C₄⋊C₄	—	188	2	no	—
406	C₄⋊C₄	—	188	2	no	—
407	C₂²⋊C₄	—	94	2	no	—
408	C₂²⋊C₄	—	188	2	no	—
409	C₂²⋊C₄	—	188	2	no	—
410	C₄²	—	47	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	1	no	—
413	C₄²	—	188	2	no	—
414	C₄²	—	188	2	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	94	1	no	—
417	C₂³	#13094070	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	47	2	no	—
420	Q₈	—	94	1	no	—
421	Q₈	C₄⋊C₄×D₄₇	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	47	2	no	—
426	D₄	—	94	2	no	—
427	D₄	—	94	2	no	—
428	D₄	—	94	1	no	—
429	D₄	C₄⋊C₄×D₄₇	1	2	yes	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	94	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	376	2	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	752	2	no	—
446	C₂×C₄	—	752	2	no	—
447	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
452	C₂×C₄	#13094071	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	47	2	no	—
456	C₈	—	47	2	no	—
457	C₈	—	94	2	no	—
458	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
459	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	94	2	no	—
466	C₂²	—	188	1	no	—
467	C₂²	—	188	1	no	—
468	C₂²	#15689603	1	1	yes	characteristic
469	C₂²	#15689757	1	1	yes	characteristic
470	C₂²	#15689831	1	1	yes	characteristic
471	C₄	—	2	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	94	4	no	—
474	C₄	—	94	2	no	—
475	C₄	—	376	2	no	—
476	C₄	—	188	2	no	—
477	C₄	—	188	2	no	—
478	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
479	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
480	C₄	#15689773	1	1	yes	characteristic
481	C₄	#15689786	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	4	2	no	—
485	C₂	—	188	2	no	—
486	C₂	#20246284	1	1	yes	characteristic
487	C₂	#20255186	1	1	yes	characteristic
488	C₂	#20255191	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689757
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1816	C₂
socle	C₂²×C₄₇	D₄²
prime radical	C₂×#13094044	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1816	D₄₇
hypocenter	C₄₇	#22692
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1816

Complements

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

N	H ≅ G/N	type
3. #20251988	C₂	semidirect
4. #20251984	C₂	semidirect
5. #20244172	C₂	semidirect
6. #20243617	C₂	semidirect
7. #20243612	C₂	semidirect
8. #20243546	C₂	semidirect
9. #20243449	C₂	semidirect
10. #20243270	C₂	semidirect
11. C₄₇×#1816	C₂	semidirect
16. #15689238	C₄	semidirect
54. #13094030	C₂×C₄	semidirect
73. #13093959	C₂×C₄	semidirect
85. #13093951	C₂×C₄	semidirect
86. #13093950	C₂×C₄	semidirect
91. C₈×Dic₄₇	C₂×C₄	semidirect
94. #131×C₄₇	C₂×C₄	semidirect
144. #10625337	C₄⋊C₄	semidirect
145. #10625336	C₄⋊C₄	semidirect
146. #10625335	C₄⋊C₄	semidirect
147. #10625334	C₄⋊C₄	semidirect
247. #1816	D₄₇	semidirect
290. C₄₇	#22692	semidirect
302. #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
C₂×#15689238	2
#20252259	2
#20251988	2
#20251984	2
#20244172	2
#20243617	2
#20243612	2
#20243546	2
#20243449	2
#20243270	2
C₄₇×#1816	2
#22692	47