Subgroups — #26185444

Order 12032.

684 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252020	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
3	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20242178	C₂	1	4	yes	maximal, complemented
5	#20242172	C₂	1	4	yes	maximal, complemented
6	#20242146	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242144	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₄₇	—	2	1	no	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689179	—	2	1	no	—
13	#15689179	C₂²	1	2	yes	—
14	#15689175	—	2	1	no	—
15	#15689175	C₂²	1	2	yes	—
16	#15689174	C₄	1	2	yes	—
17	#15689174	C₄	1	2	yes	—
18	#15689174	C₂²	1	2	yes	—
19	#15689174	C₂²	1	2	yes	—
20	#15689147	C₂²	1	1	yes	characteristic
21	#15689147	C₂²	1	1	yes	characteristic
22	#15689146	—	2	1	no	—
23	#15689145	—	2	1	no	—
24	#15689145	C₂²	1	2	yes	—
25	C₂×Dic₄₇⋊C₈	C₄	1	2	yes	—
26	C₄⋊C₈×D₄₇	—	2	1	no	—
27	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
28	#15689086	—	2	1	no	—
29	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
30	M₁₆×Dic₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	4	yes	complemented
33	#15688874	C₂²	1	4	yes	complemented
34	#15688873	C₂²	1	4	yes	complemented
35	C₄₇×#423	C₂²	1	1	yes	characteristic
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#335	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
42	C₂×#10625329	—	2	1	no	—
43	C₂×#10625329	—	2	1	no	—
44	C₂×#10625324	—	2	2	no	—
45	M₁₆×D₄₇	—	4	4	no	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
51	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₄₇	D₄	1	1	yes	characteristic
54	C₄²×D₄₇	D₄	1	1	yes	characteristic
55	C₄²×D₄₇	Q₈	1	1	yes	characteristic
56	C₄²×D₄₇	Q₈	1	1	yes	characteristic
57	C₄²×D₄₇	C₂³	1	1	yes	characteristic
58	C₄²×D₄₇	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	Dic₄₇⋊C₈	—	2	2	no	—
64	Dic₄₇⋊C₈	—	2	2	no	—
65	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
66	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
67	(C₂×D₄₇)⋊C₈	—	2	2	no	—
68	(C₂×D₄₇)⋊C₈	—	2	2	no	—
69	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
70	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
71	#13093934	—	2	2	no	—
72	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
74	C₈×Dic₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
83	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₄₇	—	2	2	no	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	4	no	—
95	C₂×C₄×D₄₇	—	4	2	no	—
96	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
108	M₁₆×C₄₇	—	4	2	no	—
109	M₁₆×C₄₇	—	4	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
129	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
130	#10625329	—	4	2	no	—
131	#10625329	—	4	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	4	2	no	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
136	#10625324	—	4	4	no	—
137	C₈×D₄₇	—	4	4	no	—
138	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	4	1	no	—
142	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₄₇	#137	1	2	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	4	1	no	—
157	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	2	1	no	—
167	C₄×D₄₇	—	2	1	no	—
168	C₄×D₄₇	—	2	1	no	—
169	C₄×D₄₇	—	2	1	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	4	1	no	—
175	C₄×D₄₇	—	4	1	no	—
176	C₄×D₄₇	#108	1	4	yes	—
177	C₈×C₄₇	—	2	4	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₈×C₄₇	—	4	2	no	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	#17817	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	#428	1	2	yes	—
187	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	1	no	—
193	C₂×D₄₇	—	4	4	no	—
194	C₂×D₄₇	C₂×#108	1	2	yes	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	#428	1	2	yes	—
198	C₄×C₄₇	C₂×#108	1	2	yes	—
199	C₄×C₄₇	#568	1	2	yes	—
200	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
202	Dic₄₇	—	2	1	no	—
203	Dic₄₇	—	2	1	no	—
204	Dic₄₇	—	2	1	no	—
205	Dic₄₇	—	2	1	no	—
206	Dic₄₇	—	2	1	no	—
207	Dic₄₇	C₂×#108	1	2	yes	—
208	#2920	—	47	1	no	—
209	C₂×#431	—	47	1	no	—
210	C₂×#423	—	47	1	no	—
211	#1574	—	47	4	no	—
212	#1573	—	47	4	no	—
213	#1567	—	47	1	no	—
214	#1567	D₄₇	1	1	yes	characteristic, complemented
215	#1566	—	47	1	no	—
216	#1566	—	47	1	no	—
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	#2905	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
220	C₂×C₄₇	C₂²×#108	1	1	yes	characteristic
221	D₄₇	—	2	2	no	—
222	D₄₇	—	4	1	no	—
223	C₂²×M₁₆	—	94	1	no	—
224	C₂²×C₄²	—	47	1	no	—
225	#432	—	47	2	no	—
226	#432	—	94	1	no	—
227	#431	—	47	2	no	—
228	#431	—	47	2	no	—
229	#431	—	47	2	no	—
230	#431	—	47	2	no	—
231	#431	—	47	2	no	—
232	#431	—	94	1	no	—
233	#423	—	47	1	no	—
234	#423	—	47	1	no	—
235	#423	—	47	2	no	—
236	#423	—	94	1	no	—
237	#423	—	94	1	no	—
238	#423	C₂×D₄₇	1	1	yes	characteristic
239	#423	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄⋊C₈	—	47	2	no	—
241	C₂×C₄⋊C₈	—	47	2	no	—
242	C₂×C₄⋊C₈	—	94	1	no	—
243	#407	—	94	1	no	—
244	C₂×C₂²⋊C₈	—	47	2	no	—
245	C₄×M₁₆	—	94	1	no	—
246	C₂×C₄×C₈	—	47	1	no	—
247	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
248	#335	—	47	4	no	—
249	#335	C₂×D₄₇	1	4	yes	complemented
250	#334	—	47	4	no	—
251	#334	—	47	4	no	—
252	C₄₇	#17817	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	47	1	no	—
254	C₂³×C₄	—	47	1	no	—
255	C₂³×C₄	—	47	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	1	no	—
260	C₂×M₁₆	—	94	1	no	—
261	C₂×M₁₆	—	188	4	no	—
262	C₂²×C₈	—	47	2	no	—
263	C₂²×C₈	—	94	2	no	—
264	C₂²×C₈	C₄×D₄₇	1	2	yes	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	47	1	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	47	4	no	—
280	C₄⋊C₈	—	47	4	no	—
281	C₄⋊C₈	—	47	2	no	—
282	C₄⋊C₈	—	47	2	no	—
283	C₄⋊C₈	—	94	2	no	—
284	C₄⋊C₈	—	94	2	no	—
285	C₄⋊C₈	—	94	1	no	—
286	C₄⋊C₈	—	94	1	no	—
287	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
288	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
289	C₂²⋊C₈	—	47	4	no	—
290	C₂²⋊C₈	—	47	4	no	—
291	C₂²⋊C₈	—	94	2	no	—
292	C₂²⋊C₈	—	94	2	no	—
293	#97	—	94	2	no	—
294	C₄×C₈	—	47	2	no	—
295	C₄×C₈	—	47	2	no	—
296	C₄×C₈	—	94	2	no	—
297	C₄×C₈	C₄×D₄₇	1	2	yes	—
298	C₄×C₈	C₂²×D₄₇	1	2	yes	—
299	C₂⁴	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	47	1	no	—
315	C₂²×C₄	—	94	4	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	188	2	no	—
319	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
322	M₁₆	—	4	2	no	—
323	M₁₆	—	4	2	no	—
324	M₁₆	—	188	4	no	—
325	M₁₆	—	188	2	no	—
326	M₁₆	—	188	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	47	4	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	188	4	no	—
334	C₂×C₈	—	188	2	no	—
335	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
336	C₄²	—	47	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	47	1	no	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	1	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	47	1	no	—
343	C₄²	—	47	1	no	—
344	C₄²	—	47	1	no	—
345	C₄²	—	47	1	no	—
346	C₄²	—	47	1	no	—
347	C₄²	—	47	1	no	—
348	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
349	C₄²	D₄×D₄₇	1	1	yes	characteristic
350	C₄²	Q₈×D₄₇	1	1	yes	characteristic
351	C₄²	C₂³×D₄₇	1	1	yes	characteristic
352	C₂³	—	47	1	no	—
353	C₂³	—	47	1	no	—
354	C₂³	—	94	2	no	—
355	C₂³	—	94	2	no	—
356	C₂³	—	188	1	no	—
357	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	47	1	no	—
361	C₂×C₄	—	47	4	no	—
362	C₂×C₄	—	47	1	no	—
363	C₂×C₄	—	47	1	no	—
364	C₂×C₄	—	47	1	no	—
365	C₂×C₄	—	47	1	no	—
366	C₂×C₄	—	47	1	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	1	no	—
374	C₂×C₄	—	94	1	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	188	1	no	—
381	C₂×C₄	—	188	1	no	—
382	C₂×C₄	—	188	1	no	—
383	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	#13094048	1	2	yes	—
387	C₂×C₄	#13094056	1	2	yes	—
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	94	4	no	—
395	C₈	—	188	2	no	—
396	C₈	—	188	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	47	2	no	—
400	C₂²	—	94	1	no	—
401	C₂²	—	94	1	no	—
402	C₂²	—	94	1	no	—
403	C₂²	—	94	1	no	—
404	C₂²	—	94	1	no	—
405	C₂²	—	188	4	no	—
406	C₂²	#15689164	1	2	yes	—
407	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	47	2	no	—
411	C₄	—	94	1	no	—
412	C₄	—	94	1	no	—
413	C₄	—	94	1	no	—
414	C₄	—	94	1	no	—
415	C₄	—	94	1	no	—
416	C₄	#15689164	1	2	yes	—
417	C₄	#108×D₄₇	1	2	yes	—
418	C₄	#15689889	1	2	yes	—
419	C₄	C₂×#13094048	1	1	yes	characteristic
420	C₄	C₂×#13094056	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	94	2	no	—
423	C₂	—	188	1	no	—
424	C₂	#20251950	1	1	yes	characteristic
425	C₂	C₂×#15689164	1	1	yes	characteristic
426	C₂	C₂×#108×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1567	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1567	D₄₇
hypocenter	C₄₇	#17817
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #20242178	C₂	semidirect
5. #20242172	C₂	semidirect
6. #20242146	C₂	semidirect
7. #20242144	C₂	semidirect
8. #20242143	C₂	semidirect
9. C₄₇×#1567	C₂	semidirect
32. #15688875	C₂²	semidirect
33. #15688874	C₂²	semidirect
34. #15688873	C₂²	semidirect
38. C₄₇×#335	C₂²	semidirect
214. #1567	D₄₇	semidirect
249. #335	C₂×D₄₇	semidirect
252. C₄₇	#17817	semidirect

Maximal subgroups

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

subgroup	index
#20252020	2
C₂×#15689174	2
#423×D₄₇	2
#20242178	2
#20242172	2
#20242146	2
#20242144	2
#20242143	2
C₄₇×#1567	2
#17817	47