Subgroups — #26185532

Order 12032.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252354	C₂	1	1	yes	maximal, characteristic
2	#20252056	C₂	1	1	yes	maximal, characteristic
3	#20251957	C₂	1	1	yes	maximal, characteristic
4	#20242178	C₂	1	2	yes	maximal, complemented
5	#20242172	C₂	1	2	yes	maximal, complemented
6	#20242164	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242160	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242154	C₂	1	2	yes	maximal, complemented
9	#20242139	C₂	1	2	yes	maximal, complemented
10	C₂×#15688874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689253	C₄	1	1	yes	characteristic
15	#15689253	C₄	1	1	yes	characteristic
16	#15689202	C₄	1	1	yes	characteristic
17	#15689202	C₄	1	1	yes	characteristic
18	#15689194	C₄	1	2	yes	—
19	#15689194	C₄	1	2	yes	—
20	#15689183	—	2	2	no	—
21	#15689179	C₂²	1	2	yes	—
22	#15689176	C₂²	1	1	yes	characteristic
23	#15689175	C₂²	1	2	yes	—
24	#15689174	C₂²	1	2	yes	—
25	#15689151	—	2	1	no	—
26	#15689148	—	2	2	no	—
27	#15689145	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
31	#15689091	—	2	1	no	—
32	#15689081	—	2	1	no	—
33	C₄×#10625324	C₂²	1	2	yes	—
34	#15688875	C₂²	1	2	yes	—
35	#15688875	C₂²	1	2	yes	—
36	#15688874	C₂²	1	1	yes	characteristic
37	#15688874	C₂²	1	1	yes	characteristic
38	#15688874	C₂²	1	1	yes	characteristic
39	#15688874	C₂²	1	1	yes	characteristic
40	#15688873	C₂²	1	2	yes	—
41	#15688873	C₂²	1	2	yes	—
42	C₄₇×#423	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	—
46	C₄₇×#335	C₂²	1	2	yes	—
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	#13094032	—	4	4	no	—
49	C₂×#10625324	—	2	2	no	—
50	C₂×#10625324	C₂×C₄	1	2	yes	—
51	C₂×#10625324	C₂×C₄	1	2	yes	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₉₄	Q₈	1	1	yes	characteristic
57	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
58	C₄×D₁₈₈	Q₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₄₇	Q₈	1	2	yes	—
61	#13093983	D₄	1	1	yes	characteristic
62	#13093981	D₄	1	2	yes	—
63	C₄²×D₄₇	C₂³	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
72	Dic₄₇⋊C₈	—	2	2	no	—
73	Dic₄₇⋊C₈	—	2	2	no	—
74	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
75	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	—	2	2	no	—
79	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
81	#13093934	—	2	2	no	—
82	#13093934	C₂×C₄	1	2	yes	—
83	#13093934	C₂×C₄	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	1	no	—
92	C₄⋊C₈×C₄₇	—	2	1	no	—
93	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
94	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
95	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	2	yes	—
103	#10625350	—	2	2	no	—
104	#10625350	—	2	2	no	—
105	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
109	C₂×Dic₉₄	C₄⋊C₄	1	1	yes	characteristic
110	M₁₆×C₄₇	—	4	2	no	—
111	M₁₆×C₄₇	—	4	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	4	1	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
125	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
126	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
127	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
129	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
130	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
132	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
133	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	4	2	no	—
139	C₂×C₄₇⋊C₈	—	4	2	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	#10625324	—	2	4	no	—
143	#10625324	—	4	2	no	—
144	#10625324	—	4	4	no	—
145	C₈×D₄₇	—	4	4	no	—
146	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₄₇	#137	1	2	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
159	C₂²⋊D₄₇	—	2	4	no	—
160	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	D₁₈₈	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	Dic₉₄	—	2	2	no	—
170	C₈×C₄₇	—	2	1	no	—
171	C₈×C₄₇	—	2	1	no	—
172	C₈×C₄₇	—	2	1	no	—
173	C₈×C₄₇	—	4	2	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	#131	1	2	yes	complemented
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	2	2	no	—
178	C₄₇⋊C₈	—	4	1	no	—
179	C₄₇⋊C₈	—	4	1	no	—
180	C₄₇⋊C₈	—	4	1	no	—
181	C₄₇⋊C₈	—	4	1	no	—
182	#17830	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	#428	1	2	yes	—
186	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₄₇	—	2	2	no	—
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	#428	1	2	yes	—
194	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
195	C₄×C₄₇	#568	1	1	yes	characteristic
196	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	2	2	no	—
200	Dic₄₇	—	2	2	no	—
201	#2965	—	47	1	no	—
202	#2925	—	47	1	no	—
203	#2906	—	47	1	no	—
204	#1574	—	47	2	no	—
205	#1573	—	47	2	no	—
206	#1571	—	47	1	no	—
207	#1570	—	47	1	no	—
208	#1569	—	47	2	no	—
209	#1567	D₄₇	1	1	yes	characteristic, complemented
210	#1565	—	47	2	no	—
211	C₂×#334	—	47	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	#2906	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
215	C₂×C₄₇	#2916	1	1	yes	characteristic
216	D₄₇	—	4	2	no	—
217	C₂×#131	—	94	1	no	—
218	C₄×#41	—	47	1	no	—
219	#446	—	47	1	no	—
220	#446	—	47	1	no	—
221	#436	—	47	1	no	—
222	#436	—	47	1	no	—
223	#435	—	47	2	no	—
224	#435	—	47	2	no	—
225	#433	—	94	2	no	—
226	#432	—	47	2	no	—
227	#431	—	47	1	no	—
228	#431	—	47	2	no	—
229	#431	—	47	2	no	—
230	#424	—	94	2	no	—
231	#424	—	94	1	no	—
232	#423	—	47	2	no	—
233	#423	C₂×D₄₇	1	1	yes	characteristic
234	#423	C₂×D₄₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	47	1	no	—
236	C₂×C₄⋊C₈	—	47	1	no	—
237	C₂×C₄⋊C₈	—	47	2	no	—
238	#408	—	94	1	no	—
239	#405	—	94	1	no	—
240	C₄×M₁₆	—	47	2	no	—
241	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
242	#335	—	47	2	no	—
243	#335	—	47	2	no	—
244	#335	C₂×D₄₇	1	2	yes	—
245	#335	C₂×D₄₇	1	2	yes	—
246	#334	—	47	2	no	—
247	#334	—	47	2	no	—
248	#334	—	47	1	no	—
249	#334	—	47	1	no	—
250	#334	—	47	1	no	—
251	#334	—	47	1	no	—
252	C₄₇	#17830	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	47	1	no	—
254	#131	—	188	4	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	47	2	no	—
258	C₂×M₁₆	—	47	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	—	94	1	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
265	C₄×Q₈	—	47	1	no	—
266	C₄×Q₈	—	47	1	no	—
267	C₄×D₄	—	47	2	no	—
268	C₄×D₄	—	47	2	no	—
269	C₄×D₄	—	47	1	no	—
270	C₄×D₄	—	47	1	no	—
271	#117	—	47	1	no	—
272	#117	—	47	2	no	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	47	2	no	—
278	C₄⋊C₈	—	47	2	no	—
279	C₄⋊C₈	—	47	1	no	—
280	C₄⋊C₈	—	47	1	no	—
281	C₄⋊C₈	—	47	1	no	—
282	C₄⋊C₈	—	47	1	no	—
283	C₄⋊C₈	—	47	1	no	—
284	C₄⋊C₈	—	47	1	no	—
285	C₄⋊C₈	—	94	2	no	—
286	C₄⋊C₈	—	94	2	no	—
287	C₄⋊C₈	—	94	1	no	—
288	C₄⋊C₈	—	94	1	no	—
289	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
290	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
291	C₂²⋊C₈	—	47	2	no	—
292	C₂²⋊C₈	—	47	2	no	—
293	C₂²⋊C₈	—	47	2	no	—
294	C₂²⋊C₈	—	94	2	no	—
295	C₂²⋊C₈	—	94	2	no	—
296	#97	—	47	2	no	—
297	#97	—	47	2	no	—
298	#97	—	94	2	no	—
299	C₄×C₈	—	47	2	no	—
300	C₄×C₈	—	94	2	no	—
301	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
302	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
305	#41	—	94	2	no	—
306	#41	—	94	2	no	—
307	C₂×Q₈	—	47	1	no	—
308	C₂×D₄	—	47	2	no	—
309	C₂×D₄	—	47	1	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	47	2	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	94	4	no	—
319	M₁₆	—	188	2	no	—
320	M₁₆	—	188	4	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	188	4	no	—
332	C₂×C₈	—	188	2	no	—
333	C₂×C₈	—	188	2	no	—
334	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₄⋊C₄	—	47	2	no	—
339	C₄⋊C₄	—	47	2	no	—
340	C₄⋊C₄	—	47	1	no	—
341	C₄⋊C₄	—	47	1	no	—
342	C₂²⋊C₄	—	47	2	no	—
343	C₂²⋊C₄	—	47	2	no	—
344	C₂²⋊C₄	—	47	2	no	—
345	C₄²	—	47	2	no	—
346	C₄²	—	47	2	no	—
347	C₄²	—	47	2	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	2	no	—
353	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
354	Q₈	—	94	2	no	—
355	D₄	—	94	4	no	—
356	D₄	—	94	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	47	2	no	—
361	C₂×C₄	—	47	2	no	—
362	C₂×C₄	—	47	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	#13094048	1	2	yes	—
372	C₂×C₄	#13094056	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	94	2	no	—
382	C₈	—	94	2	no	—
383	C₈	—	188	1	no	—
384	C₈	—	188	1	no	—
385	C₈	—	188	1	no	—
386	C₈	—	188	1	no	—
387	C₈	#13094032	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	94	2	no	—
391	C₂²	—	94	2	no	—
392	C₂²	—	94	2	no	—
393	C₂²	#15689164	1	2	yes	—
394	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	94	2	no	—
399	C₄	—	94	2	no	—
400	C₄	—	94	2	no	—
401	C₄	#15689164	1	2	yes	—
402	C₄	C₂×#13094032	1	1	yes	characteristic
403	C₄	#15689889	1	1	yes	characteristic
404	C₄	C₂×#13094048	1	1	yes	characteristic
405	C₄	C₂×#13094056	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	188	2	no	—
408	C₂	#20251957	1	1	yes	characteristic
409	C₂	C₂×#15689164	1	1	yes	characteristic
410	C₂	#20251996	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	C₂×#10625350	D₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1567	D₄₇
hypocenter	C₄₇	#17830
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. #20242164	C₂	semidirect
7. #20242160	C₂	semidirect
8. #20242154	C₂	semidirect
9. #20242139	C₂	semidirect
10. C₂×#15688874	C₂	semidirect
11. C₄₇×#1567	C₂	semidirect
175. C₈×C₄₇	#131	semidirect
209. #1567	D₄₇	semidirect
252. C₄₇	#17830	semidirect
387. C₈	#13094032	semidirect

Maximal subgroups

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

subgroup	index
#20252354	2
#20252056	2
#20251957	2
#20242178	2
#20242172	2
#20242164	2
#20242160	2
#20242154	2
#20242139	2
C₂×#15688874	2
C₄₇×#1567	2
#17830	47