Subgroups — #26234725

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689246	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689244	C₂	1	1	yes	maximal, characteristic
3	#20252159	C₂	1	1	yes	maximal, characteristic
4	#20251955	C₂	1	2	yes	maximal, complemented
5	#20244142	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243664	C₂	1	2	yes	maximal, complemented
7	#20243662	C₂	1	2	yes	maximal, complemented
8	#20243558	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243407	C₂	1	2	yes	maximal, complemented
10	#20243256	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	C₂×#13094030	C₂²	1	2	yes	—
15	#15689591	C₂²	1	2	yes	—
16	#15689246	—	2	4	no	—
17	#15689244	—	2	4	no	—
18	#15689217	C₄	1	1	yes	characteristic, complemented
19	#15689217	C₄	1	1	yes	characteristic, complemented
20	#15689210	C₄	1	2	yes	complemented
21	#15689210	C₄	1	2	yes	complemented
22	#15689205	C₄	1	1	yes	characteristic, complemented
23	#15689205	C₄	1	1	yes	characteristic, complemented
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	C₂×#13093959	C₂²	1	2	yes	—
26	#15689150	C₂²	1	2	yes	—
27	#15689148	—	2	2	no	—
28	#15689148	—	2	2	no	—
29	#15689146	C₂²	1	2	yes	—
30	#15689145	—	2	2	no	—
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₄₇	—	2	2	no	—
33	C₂×#13093952	C₂²	1	2	yes	—
34	C₂×#13093950	C₂²	1	2	yes	—
35	#15689117	C₂²	1	2	yes	—
36	C₂×#13093934	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
39	#15688882	C₂²	1	2	yes	—
40	#15688878	C₂²	1	1	yes	characteristic
41	#15688877	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#427	C₂²	1	1	yes	characteristic
44	C₄₇×#424	C₂²	1	2	yes	—
45	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
46	C₄₇×#339	C₂²	1	2	yes	—
47	C₂×#10625350	C₂³	1	2	yes	—
48	#13094046	D₄	1	4	yes	—
49	#13094046	Q₈	1	4	yes	—
50	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
53	#13094032	—	2	4	no	—
54	#13094032	—	4	2	no	—
55	#13094030	—	2	4	no	—
56	#13094030	—	4	2	no	—
57	C₂×#10625329	C₂³	1	2	yes	—
58	C₂×#10625324	—	2	2	no	—
59	C₂×#10625324	—	2	2	no	—
60	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₄₇	—	2	2	no	—
63	C₂×C₈×D₄₇	—	2	2	no	—
64	#13093989	C₂×C₄	1	2	yes	—
65	#13093989	C₂×C₄	1	2	yes	—
66	#13093986	C₂×C₄	1	2	yes	—
67	#13093986	C₂×C₄	1	2	yes	—
68	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
69	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
70	#13093981	—	2	2	no	—
71	C₂×Dic₄₇⋊C₄	—	2	1	no	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
74	C₄²×D₄₇	—	2	2	no	—
75	#13093960	—	2	2	no	—
76	#13093959	—	4	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	D₄	1	2	yes	—
82	Dic₄₇⋊C₈	D₄	1	2	yes	—
83	#13093952	—	2	4	no	—
84	#13093950	—	2	4	no	—
85	#13093947	C₂×C₄	1	2	yes	—
86	#13093947	C₂×C₄	1	2	yes	—
87	#13093944	C₂×C₄	1	2	yes	—
88	#13093944	C₂×C₄	1	2	yes	—
89	#13093934	—	2	2	no	—
90	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₄₇⋊#95	—	2	1	no	—
95	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	#117×C₄₇	C₂³	1	2	yes	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#108×C₄₇	—	2	2	no	—
101	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
102	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
103	#106×C₄₇	C₂×C₄	1	2	yes	—
104	C₄⋊C₈×C₄₇	—	2	2	no	—
105	C₄⋊C₈×C₄₇	—	2	2	no	—
106	#97×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂²×Dic₄₇	#41	1	1	yes	characteristic
112	C₂²×Dic₄₇	#41	1	1	yes	characteristic
113	#10625350	—	2	2	no	—
114	#10625350	—	2	2	no	—
115	#10625350	C₂×D₄	1	4	yes	—
116	#10625350	C₂×Q₈	1	4	yes	—
117	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	2	no	—
139	(C₂×D₄₇)⋊C₄	—	2	2	no	—
140	Dic₄₇⋊C₄	—	2	2	no	—
141	Dic₄₇⋊C₄	—	2	2	no	—
142	Dic₄₇⋊C₄	—	4	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₄×Dic₄₇	—	2	1	no	—
147	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
151	#10625329	—	2	2	no	—
152	#10625329	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
161	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
162	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
163	#10625325	C₄⋊C₄	1	8	yes	complemented
164	#10625324	—	4	4	no	—
165	#10625324	—	4	4	no	—
166	C₈×D₄₇	—	4	4	no	—
167	C₈×D₄₇	—	4	4	no	—
168	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂²×D₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
181	C₂²⋊D₄₇	—	2	4	no	—
182	C₂²⋊D₄₇	—	2	4	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	C₂×Dic₄₇	—	4	1	no	—
189	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
193	D₁₈₈	—	2	2	no	—
194	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
195	C₄×D₄₇	—	2	4	no	—
196	C₄×D₄₇	—	2	4	no	—
197	C₄×D₄₇	—	4	4	no	—
198	C₄×D₄₇	—	8	2	no	—
199	Dic₉₄	—	2	2	no	—
200	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
201	C₈×C₄₇	—	2	2	no	—
202	C₈×C₄₇	—	4	2	no	—
203	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
204	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
205	C₄₇⋊C₈	—	2	1	no	—
206	C₄₇⋊C₈	—	2	1	no	—
207	C₄₇⋊C₈	—	2	2	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	#22686	—	47	1	no	maximal, Sylow
210	C₂²×C₄₇	—	2	1	no	—
211	C₂²×C₄₇	—	2	1	no	—
212	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂²×C₄₇	#547	1	1	yes	characteristic
214	C₂²×C₄₇	#554	1	1	yes	characteristic
215	C₂×D₄₇	—	2	4	no	—
216	C₂×D₄₇	—	4	2	no	—
217	C₂×D₄₇	—	4	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	8	1	no	—
221	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₄×C₄₇	#520	1	1	yes	characteristic
223	C₄×C₄₇	D₄²	1	1	yes	characteristic
224	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
225	Dic₄₇	—	2	4	no	—
226	Dic₄₇	—	2	1	no	—
227	Dic₄₇	—	2	1	no	—
228	Dic₄₇	—	2	1	no	—
229	Dic₄₇	—	8	1	no	—
230	Dic₄₇	#444	1	2	yes	complemented
231	C₂×#444	—	47	1	no	—
232	C₂×#444	—	47	1	no	—
233	C₄×#135	—	47	1	no	—
234	#2906	—	47	2	no	—
235	#1946	—	47	1	no	—
236	#1946	D₄₇	1	1	yes	characteristic, complemented
237	#1866	—	47	2	no	—
238	#1866	—	47	2	no	—
239	#1848	—	47	1	no	—
240	#1806	—	47	2	no	—
241	#1770	—	47	1	no	—
242	C₂×C₄₇	—	2	1	no	—
243	C₂×C₄₇	—	2	1	no	—
244	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
246	C₂×C₄₇	#2957	1	1	yes	characteristic
247	D₄₇	—	4	4	no	—
248	C₂×#135	—	47	1	no	—
249	C₂×#131	—	47	2	no	—
250	C₂×#131	—	47	2	no	—
251	C₄×#41	—	47	2	no	—
252	#444	—	94	4	no	—
253	#444	—	94	4	no	—
254	C₄×Q₁₆	—	47	1	no	—
255	C₄×Q₁₆	—	47	1	no	—
256	C₄×SD₁₆	—	47	2	no	—
257	C₄×SD₁₆	—	47	2	no	—
258	C₄×D₈	—	47	1	no	—
259	C₄×D₈	—	47	1	no	—
260	C₂×#108	—	47	1	no	—
261	C₂×#108	—	47	2	no	—
262	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
263	#427	C₂×D₄₇	1	1	yes	characteristic
264	#424	—	47	2	no	—
265	#424	—	94	2	no	—
266	#424	—	94	2	no	—
267	#424	C₂×D₄₇	1	2	yes	—
268	#423	—	47	2	no	—
269	#423	—	94	2	no	—
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	—	94	2	no	—
272	C₂×#104	—	47	2	no	—
273	C₂×#104	—	47	2	no	—
274	#416	—	47	2	no	—
275	C₂×#97	—	47	1	no	—
276	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
277	C₂×C₄×C₈	—	47	1	no	—
278	C₄×C₄⋊C₄	—	47	1	no	—
279	#339	—	47	2	no	—
280	#339	C₂×D₄₇	1	2	yes	—
281	#336	—	47	1	no	—
282	#336	—	47	1	no	—
283	C₄₇	#22686	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	47	2	no	—
285	#135	—	47	4	no	—
286	#135	—	47	4	no	—
287	C₂×Q₁₆	—	47	1	no	—
288	C₂×SD₁₆	—	47	2	no	—
289	C₂×D₈	—	47	1	no	—
290	#131	—	94	4	no	—
291	#131	—	94	4	no	—
292	#131	—	188	2	no	—
293	#131	—	188	2	no	—
294	C₂×M₁₆	—	47	2	no	—
295	C₂×M₁₆	—	94	2	no	—
296	C₂×M₁₆	—	94	2	no	—
297	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	94	2	no	—
301	C₂²×C₈	—	94	2	no	—
302	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₄×Q₈	—	47	2	no	—
305	C₄×Q₈	—	47	2	no	—
306	C₄×D₄	—	47	2	no	—
307	C₄×D₄	—	47	2	no	—
308	C₄×D₄	—	94	2	no	—
309	C₄×D₄	—	94	2	no	—
310	#117	—	94	2	no	—
311	#117	C₂²×D₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	—	94	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	94	2	no	—
316	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
317	#108	—	2	2	no	—
318	#108	—	94	2	no	—
319	#108	—	188	2	no	—
320	#107	C₄×D₄₇	1	1	yes	characteristic
321	#107	C₄×D₄₇	1	1	yes	characteristic
322	#106	C₄×D₄₇	1	2	yes	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	47	2	no	—
326	C₄⋊C₈	—	47	2	no	—
327	C₄⋊C₈	—	94	2	no	—
328	C₄⋊C₈	—	94	2	no	—
329	C₄⋊C₈	—	94	2	no	—
330	C₄⋊C₈	—	94	2	no	—
331	#104	—	94	4	no	—
332	#104	—	94	4	no	—
333	#103	—	47	2	no	—
334	#103	—	47	2	no	—
335	#102	—	47	2	no	—
336	#102	—	47	2	no	—
337	#97	—	2	2	no	—
338	#97	—	94	2	no	—
339	C₄×C₈	—	47	1	no	—
340	C₄×C₈	—	47	1	no	—
341	C₄×C₈	—	47	1	no	—
342	C₄×C₈	—	47	1	no	—
343	#95	—	94	1	no	—
344	#41	—	47	4	no	—
345	#41	—	47	4	no	—
346	#41	—	94	2	no	—
347	#41	—	94	2	no	—
348	C₂×Q₈	—	47	2	no	—
349	C₂×D₄	—	47	2	no	—
350	C₂×D₄	—	94	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	1	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	2	no	—
357	C₂²×C₄	—	94	1	no	—
358	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
359	Q₁₆	—	47	4	no	—
360	SD₁₆	—	47	8	no	—
361	D₈	—	47	4	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	94	2	no	—
365	M₁₆	—	94	2	no	—
366	M₁₆	—	188	4	no	—
367	M₁₆	—	188	4	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	47	1	no	—
372	C₂×C₈	—	47	1	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	188	4	no	—
380	C₂×C₈	—	188	4	no	—
381	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₈	D₄×D₄₇	1	2	yes	—
384	C₂×C₈	D₄×D₄₇	1	2	yes	—
385	C₂×C₈	Q₈×D₄₇	1	2	yes	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	94	2	no	—
388	C₄⋊C₄	—	188	2	no	—
389	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
390	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	94	2	no	—
393	C₂²⋊C₄	—	94	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	47	1	no	—
398	C₄²	—	47	1	no	—
399	C₄²	—	47	1	no	—
400	C₄²	—	47	1	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	2	no	—
403	C₄²	—	94	1	no	—
404	C₄²	—	94	1	no	—
405	C₂³	—	94	2	no	—
406	C₂³	#41×D₄₇	1	1	yes	characteristic
407	Q₈	—	47	4	no	—
408	Q₈	—	94	2	no	—
409	D₄	—	47	4	no	—
410	D₄	—	94	4	no	—
411	D₄	—	94	4	no	—
412	D₄	—	94	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	47	1	no	—
419	C₂×C₄	—	47	1	no	—
420	C₂×C₄	—	47	1	no	—
421	C₂×C₄	—	47	1	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	4	no	—
425	C₂×C₄	—	94	4	no	—
426	C₂×C₄	—	376	2	no	—
427	C₂×C₄	—	188	4	no	—
428	C₂×C₄	—	188	1	no	—
429	C₂×C₄	—	188	1	no	—
430	C₂×C₄	—	188	1	no	—
431	C₂×C₄	—	188	1	no	—
432	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
436	C₂×C₄	#13094070	1	1	yes	characteristic
437	C₂×C₄	#13094072	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₈	—	94	2	no	—
441	C₈	—	94	1	no	—
442	C₈	—	94	1	no	—
443	C₈	—	188	2	no	—
444	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
445	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	94	4	no	—
449	C₂²	—	188	2	no	—
450	C₂²	—	188	2	no	—
451	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
452	C₂²	#15689775	1	1	yes	characteristic
453	C₂²	#15689829	1	1	yes	characteristic
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	47	2	no	—
458	C₄	—	94	4	no	—
459	C₄	—	94	1	no	—
460	C₄	—	94	1	no	—
461	C₄	—	94	1	no	—
462	C₄	—	376	1	no	—
463	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
464	C₄	#15689605	1	1	yes	characteristic
465	C₄	#15689757	1	1	yes	characteristic
466	C₄	#15689788	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	188	4	no	—
470	C₂	#20246289	1	1	yes	characteristic
471	C₂	#444×D₄₇	1	1	yes	characteristic
472	C₂	#20252302	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1946	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1946	D₄₇
hypocenter	C₄₇	#22686
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1946

Complements

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

N	H ≅ G/N	type
4. #20251955	C₂	semidirect
5. #20244142	C₂	semidirect
6. #20243664	C₂	semidirect
7. #20243662	C₂	semidirect
8. #20243558	C₂	semidirect
9. #20243407	C₂	semidirect
10. #20243256	C₂	semidirect
11. C₄₇×#1946	C₂	semidirect
18. #15689217	C₄	semidirect
19. #15689217	C₄	semidirect
20. #15689210	C₄	semidirect
21. #15689210	C₄	semidirect
22. #15689205	C₄	semidirect
23. #15689205	C₄	semidirect
161. Dic₁₈₈	C₄⋊C₄	semidirect
162. D₃₇₆	C₄⋊C₄	semidirect
163. #10625325	C₄⋊C₄	semidirect
230. Dic₄₇	#444	semidirect
236. #1946	D₄₇	semidirect
283. C₄₇	#22686	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689246	2
C₂×#15689244	2
#20252159	2
#20251955	2
#20244142	2
#20243664	2
#20243662	2
#20243558	2
#20243407	2
#20243256	2
C₄₇×#1946	2
#22686	47