Subgroups — #26234530

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#20252123	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
4	C₂×#108×D₄₇	C₂	1	2	yes	maximal, complemented
5	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243594	C₂	1	2	yes	maximal, complemented
7	#20243591	C₂	1	2	yes	maximal, complemented
8	#20243559	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243425	C₂	1	2	yes	maximal, complemented
10	C₄×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
13	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
14	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	#15689202	—	2	1	no	—
17	#15689200	—	2	1	no	—
18	#15689196	—	2	2	no	—
19	#15689193	—	2	2	no	—
20	C₈×D₁₈₈	—	2	1	no	—
21	#15689188	—	2	1	no	—
22	#15689188	C₄	1	4	yes	—
23	#15689188	C₄	1	2	yes	—
24	#15689188	C₄	1	2	yes	—
25	C₂×#13093960	C₂²	1	2	yes	—
26	C₂×#13093959	C₂²	1	2	yes	—
27	C₂×#13093959	C₂²	1	1	yes	characteristic
28	C₂×#13093959	C₂²	1	2	yes	—
29	C₂×#13093959	C₂²	1	1	yes	characteristic
30	#108×D₄₇	—	2	8	no	—
31	#15689147	C₂²	1	1	yes	characteristic
32	#15689086	C₂²	1	2	yes	—
33	#15689086	C₂²	1	2	yes	—
34	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	#15688888	C₂²	1	2	yes	—
38	#15688887	C₂²	1	1	yes	characteristic
39	#15688887	C₂²	1	1	yes	characteristic
40	C₂×#108×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#423	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#341	C₂²	1	2	yes	—
45	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
47	C₂×#10625329	C₂³	1	1	yes	characteristic
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂×#10625329	C₂³	1	1	yes	characteristic
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	—	2	2	no	—
52	M₁₆×D₄₇	—	2	4	no	—
53	M₁₆×D₄₇	—	2	4	no	—
54	M₁₆×D₄₇	—	4	2	no	—
55	M₁₆×D₄₇	—	4	2	no	—
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₇	—	2	4	no	—
59	C₂×C₈×D₄₇	—	2	4	no	—
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
64	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
65	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
67	C₄×D₁₈₈	D₄	1	1	yes	characteristic
68	C₄×D₁₈₈	D₄	1	2	yes	—
69	C₄×D₁₈₈	D₄	1	1	yes	characteristic
70	C₂×C₄⋊Dic₄₇	Q₈	1	1	yes	characteristic
71	C₂×(C₂×D₄₇)⋊C₄	Q₈	1	2	yes	—
72	#13093960	—	2	4	no	—
73	#13093959	—	2	4	no	—
74	#13093959	—	2	2	no	—
75	#13093959	—	4	2	no	—
76	#13093959	D₄	1	4	yes	complemented
77	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	(C₂×D₄₇)⋊C₈	—	2	2	no	—
80	(C₂×D₄₇)⋊C₈	—	2	2	no	—
81	(C₂×D₄₇)⋊C₈	—	2	2	no	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
84	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
85	#13093935	—	2	1	no	—
86	C₄×C₄₇⋊C₈	—	2	1	no	—
87	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
88	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
91	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	#108×C₄₇	—	2	4	no	—
95	C₄⋊C₈×C₄₇	—	2	1	no	—
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
98	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
99	#97×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	—	2	1	no	—
101	C₂³×D₄₇	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂×Q₈	1	2	yes	—
106	C₂×D₁₈₈	—	2	4	no	—
107	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
108	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
109	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
118	M₁₆×C₄₇	—	2	1	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	M₁₆×C₄₇	—	2	1	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	1	no	—
123	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
135	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
136	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
137	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
138	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
139	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
141	#10625329	—	2	1	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	2	1	no	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	1	no	—
146	#10625329	C₂×D₄	1	2	yes	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	#41	1	2	yes	—
156	#10625324	—	4	4	no	—
157	#10625324	—	4	4	no	—
158	C₈×D₄₇	—	2	8	no	—
159	C₈×D₄₇	—	2	8	no	—
160	C₈×D₄₇	—	4	4	no	—
161	C₈×D₄₇	—	4	4	no	—
162	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	—	2	2	no	—
165	C₂²×D₄₇	—	2	4	no	—
166	C₂²×D₄₇	—	4	2	no	—
167	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂×#41	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	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
184	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
185	D₁₈₈	—	2	4	no	—
186	D₁₈₈	—	2	2	no	—
187	D₁₈₈	#108	1	4	yes	complemented
188	C₄×D₄₇	—	2	2	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	2	no	—
192	C₄×D₄₇	—	2	2	no	—
193	C₄×D₄₇	—	2	2	no	—
194	C₄×D₄₇	—	2	2	no	—
195	C₄×D₄₇	—	2	2	no	—
196	C₈×C₄₇	—	2	4	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₈×C₄₇	—	4	1	no	—
200	C₄₇⋊C₈	—	2	2	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	—	4	1	no	—
204	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
205	D₄×#108	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	1	no	—
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
210	C₂²×C₄₇	#554	1	1	yes	characteristic
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	2	2	no	—
216	C₂×D₄₇	—	4	4	no	—
217	C₂×D₄₇	—	4	4	no	—
218	C₂×D₄₇	C₂×#108	1	4	yes	complemented
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	C₂×#108	1	2	yes	complemented
223	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₄₇	#520	1	1	yes	characteristic
225	C₄×C₄₇	D₄²	1	1	yes	characteristic
226	C₄×C₄₇	#547	1	1	yes	characteristic
227	Dic₄₇	—	2	2	no	—
228	Dic₄₇	—	2	2	no	—
229	D₄×M₁₆	—	47	1	no	—
230	D₄×M₁₆	—	47	1	no	—
231	C₂×C₈×D₄	—	47	1	no	—
232	C₂²×#108	—	47	2	no	—
233	#1950	—	47	1	no	—
234	#1950	D₄₇	1	1	yes	characteristic, complemented
235	#1855	—	47	2	no	—
236	#1855	—	47	2	no	—
237	#1848	—	47	1	no	—
238	#1810	—	47	2	no	—
239	C₄×#108	—	47	1	no	—
240	C₂×C₄₇	—	2	1	no	—
241	C₂×C₄₇	—	2	1	no	—
242	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
244	C₂×C₄₇	#2916	1	1	yes	characteristic
245	D₄₇	—	2	4	no	—
246	D₄₇	—	4	2	no	—
247	C₂²×M₁₆	—	47	2	no	—
248	C₂²×M₁₆	—	47	2	no	—
249	C₂³×C₈	—	47	2	no	—
250	C₂×C₄×D₄	—	47	1	no	—
251	#436	—	94	1	no	—
252	#436	—	94	1	no	—
253	#435	—	94	2	no	—
254	#435	—	94	2	no	—
255	C₈×D₄	—	47	2	no	—
256	C₈×D₄	—	47	4	no	—
257	C₈×D₄	—	47	2	no	—
258	C₈×D₄	—	94	1	no	—
259	C₈×D₄	—	94	1	no	—
260	C₂×#108	—	47	1	no	—
261	C₂×#108	—	47	1	no	—
262	C₂×#108	—	47	2	no	—
263	C₂×#108	—	47	2	no	—
264	C₂×#108	—	47	2	no	—
265	C₂×#108	—	94	8	no	—
266	C₂×#108	C₂×D₄₇	1	2	yes	—
267	#423	—	47	1	no	—
268	#423	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
270	#407	—	47	2	no	—
271	#407	—	47	2	no	—
272	C₂×C₂²⋊C₈	—	47	2	no	—
273	C₄×M₁₆	—	47	1	no	—
274	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
275	C₂×C₄×C₈	—	47	1	no	—
276	#341	—	47	1	no	—
277	#341	—	47	1	no	—
278	#341	—	47	2	no	—
279	#341	C₂×D₄₇	1	2	yes	—
280	C₄₇	D₄×#108	1	1	yes	characteristic, complemented, Sylow
281	C₂²×D₄	—	47	1	no	—
282	C₂³×C₄	—	47	2	no	—
283	C₂×M₁₆	—	47	1	no	—
284	C₂×M₁₆	—	47	2	no	—
285	C₂×M₁₆	—	47	1	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	—	94	4	no	—
289	C₂×M₁₆	—	94	4	no	—
290	C₂×M₁₆	—	188	2	no	—
291	C₂×M₁₆	—	188	2	no	—
292	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
293	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	4	no	—
298	C₂²×C₈	—	47	4	no	—
299	C₂²×C₈	—	94	4	no	—
300	C₂²×C₈	—	94	4	no	—
301	C₂²×C₈	—	94	2	no	—
302	C₂²×C₈	—	94	2	no	—
303	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
304	C₄×D₄	—	47	1	no	—
305	C₄×D₄	—	47	2	no	—
306	C₄×D₄	—	47	1	no	—
307	C₄×D₄	—	47	1	no	—
308	C₄×D₄	—	47	2	no	—
309	C₄×D₄	—	47	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₂²⋊C₄	—	47	2	no	—
312	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
313	#108	—	2	4	no	—
314	#108	—	47	4	no	—
315	#108	—	94	4	no	—
316	#108	—	94	2	no	—
317	#108	—	94	4	no	—
318	#108	—	188	2	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	94	1	no	—
322	C₄⋊C₈	—	94	1	no	—
323	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
324	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
325	C₂²⋊C₈	—	47	4	no	—
326	C₂²⋊C₈	—	47	4	no	—
327	C₂²⋊C₈	—	94	2	no	—
328	C₂²⋊C₈	—	94	2	no	—
329	C₂²⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	2	no	—
331	#97	—	2	1	no	—
332	#97	—	94	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	47	2	no	—
335	C₄×C₈	—	47	2	no	—
336	C₄×C₈	—	94	1	no	—
337	C₂⁴	—	47	2	no	—
338	C₂×D₄	—	47	1	no	—
339	C₂×D₄	—	47	2	no	—
340	C₂×D₄	—	47	1	no	—
341	C₂×D₄	—	94	4	no	—
342	C₂²×C₄	—	47	2	no	—
343	C₂²×C₄	—	47	2	no	—
344	C₂²×C₄	—	47	2	no	—
345	C₂²×C₄	—	47	2	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	94	2	no	—
348	C₂²×C₄	—	94	2	no	—
349	C₂²×C₄	—	94	2	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	47	2	no	—
360	M₁₆	—	94	1	no	—
361	M₁₆	—	94	2	no	—
362	M₁₆	—	94	1	no	—
363	M₁₆	—	94	2	no	—
364	M₁₆	—	94	1	no	—
365	M₁₆	—	188	4	no	—
366	M₁₆	—	188	4	no	—
367	M₁₆	D₄×D₄₇	1	2	yes	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	47	2	no	—
375	C₂×C₈	—	47	2	no	—
376	C₂×C₈	—	47	2	no	—
377	C₂×C₈	—	94	8	no	—
378	C₂×C₈	—	94	8	no	—
379	C₂×C₈	—	94	1	no	—
380	C₂×C₈	—	94	1	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	94	1	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	188	4	no	—
385	C₂×C₈	—	188	4	no	—
386	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
387	C₄⋊C₄	—	47	2	no	—
388	C₄⋊C₄	—	47	1	no	—
389	C₄⋊C₄	—	47	1	no	—
390	C₂²⋊C₄	—	47	2	no	—
391	C₂²⋊C₄	—	47	2	no	—
392	C₂²⋊C₄	—	47	2	no	—
393	C₂²⋊C₄	—	47	2	no	—
394	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
395	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
396	C₄²	D₄×D₄₇	1	1	yes	characteristic
397	C₄²	D₄×D₄₇	1	1	yes	characteristic
398	C₂³	—	47	2	no	—
399	C₂³	—	47	2	no	—
400	C₂³	—	94	4	no	—
401	C₂³	—	94	2	no	—
402	C₂³	—	94	2	no	—
403	C₂³	—	188	2	no	—
404	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
405	D₄	—	47	4	no	—
406	D₄	—	94	4	no	—
407	D₄	—	94	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	47	2	no	—
411	C₂×C₄	—	47	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
425	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
430	C₂×C₄	#13094070	1	1	yes	characteristic
431	C₂×C₄	#13094072	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	4	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	47	4	no	—
437	C₈	—	94	2	no	—
438	C₈	—	94	2	no	—
439	C₈	—	188	2	no	—
440	C₈	—	188	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	47	4	no	—
444	C₂²	—	94	2	no	—
445	C₂²	—	94	2	no	—
446	C₂²	—	94	2	no	—
447	C₂²	—	94	2	no	—
448	C₂²	—	94	2	no	—
449	C₂²	—	188	4	no	—
450	C₂²	—	188	4	no	—
451	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
452	C₂²	#15689788	1	1	yes	characteristic
453	C₂²	#15689829	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	94	2	no	—
458	C₄	—	94	2	no	—
459	C₄	#108×D₄₇	1	2	yes	complemented
460	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
461	C₄	#15689605	1	1	yes	characteristic
462	C₄	#15689757	1	1	yes	characteristic
463	C₄	#15689775	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	94	4	no	—
467	C₂	—	188	2	no	—
468	C₂	#20246289	1	1	yes	characteristic
469	C₂	C₂×#108×D₄₇	1	1	yes	characteristic
470	C₂	#20251998	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×#1950	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×D₁₈₈	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1950	D₄₇
hypocenter	C₄₇	D₄×#108
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. C₂×#108×D₄₇	C₂	semidirect
5. #20244164	C₂	semidirect
6. #20243594	C₂	semidirect
7. #20243591	C₂	semidirect
8. #20243559	C₂	semidirect
9. #20243425	C₂	semidirect
10. C₄×#13093959	C₂	semidirect
11. C₄₇×#1950	C₂	semidirect
76. #13093959	D₄	semidirect
187. D₁₈₈	#108	semidirect
218. C₂×D₄₇	C₂×#108	semidirect
222. C₄×C₄₇	C₂×#108	semidirect
234. #1950	D₄₇	semidirect
280. C₄₇	D₄×#108	semidirect
459. C₄	#108×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×D₁₈₈	2
#20252123	2
C₂×#15689188	2
C₂×#108×D₄₇	2
#20244164	2
#20243594	2
#20243591	2
#20243559	2
#20243425	2
C₄×#13093959	2
C₄₇×#1950	2
D₄×#108	47