Subgroups — #26185476

Order 12032.

616 conjugacy classes of subgroups.

The subgroup lattice has 458 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	#20252019	C₂	1	1	yes	maximal, characteristic
3	#20252018	C₂	1	1	yes	maximal, characteristic
4	#20242178	C₂	1	2	yes	maximal, complemented
5	#20242175	C₂	1	2	yes	maximal, complemented
6	#20242167	C₂	1	2	yes	maximal, complemented
7	#20242165	C₂	1	2	yes	maximal, complemented
8	#20242156	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242155	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
13	#15689180	C₂²	1	1	yes	characteristic
14	#15689179	—	2	1	no	—
15	#15689179	C₂²	1	2	yes	—
16	#15689178	—	2	1	no	—
17	#15689178	C₄	1	2	yes	—
18	#15689178	C₄	1	2	yes	—
19	#15689175	—	2	1	no	—
20	#15689175	C₂²	1	2	yes	—
21	#15689175	C₂²	1	1	yes	characteristic
22	#15689175	C₂²	1	1	yes	characteristic
23	#15689174	C₂²	1	2	yes	—
24	#15689174	C₂²	1	2	yes	—
25	#15689173	—	2	1	no	—
26	#15689147	C₂²	1	1	yes	characteristic
27	#15689146	C₄	1	2	yes	—
28	#15689145	C₂²	1	1	yes	characteristic
29	#15689145	C₂²	1	1	yes	characteristic
30	#15689086	—	2	1	no	—
31	#15689086	C₄	1	2	yes	—
32	#15689085	—	2	1	no	—
33	C₄×#10625329	C₂²	1	1	yes	characteristic
34	#15689075	—	2	1	no	—
35	M₁₆×Dic₄₇	—	2	1	no	—
36	#15688876	C₂²	1	2	yes	complemented
37	#15688875	C₂²	1	2	yes	complemented
38	#15688875	C₂²	1	2	yes	complemented
39	#15688874	C₂²	1	2	yes	complemented
40	#15688873	C₂²	1	2	yes	complemented
41	#15688873	C₂²	1	2	yes	complemented
42	C₄₇×#432	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	complemented
46	C₄₇×#334	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	C₂×C₄	1	2	yes	—
52	C₂×#10625324	—	2	1	no	—
53	C₂×#10625324	—	2	1	no	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	Q₈	1	1	yes	characteristic
57	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₄₇	D₄	1	1	yes	characteristic
60	C₄²×D₄₇	D₄	1	1	yes	characteristic
61	C₄²×D₄₇	Q₈	1	1	yes	characteristic
62	C₄²×D₄₇	Q₈	1	1	yes	characteristic
63	C₄²×D₄₇	C₂³	1	1	yes	characteristic
64	C₄²×D₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₄₇⋊C₈	—	2	1	no	—
70	Dic₄₇⋊C₈	—	2	1	no	—
71	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
72	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
74	(C₂×D₄₇)⋊C₈	—	2	1	no	—
75	(C₂×D₄₇)⋊C₈	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
79	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
80	#13093935	—	2	1	no	—
81	#13093935	C₂×C₄	1	2	yes	—
82	#13093934	—	2	2	no	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₄₇	—	2	2	no	—
85	C₈×Dic₄₇	—	2	1	no	—
86	C₈×Dic₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	1	no	—
91	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	#97×C₄₇	—	2	1	no	—
96	#97×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₄₇	C₂³	1	2	yes	—
98	C₂³×D₄₇	C₄⋊C₄	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	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	—	4	2	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×C₄×D₄₇	—	4	1	no	—
108	C₂×C₄×D₄₇	—	4	1	no	—
109	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
121	M₁₆×C₄₇	—	4	2	no	—
122	M₁₆×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
127	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
142	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
143	#10625329	—	4	2	no	—
144	#10625329	—	4	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
149	#10625324	—	4	2	no	—
150	#10625324	—	4	2	no	—
151	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×D₄₇	—	4	1	no	—
153	C₂²×D₄₇	—	4	1	no	—
154	C₂²×D₄₇	—	4	1	no	—
155	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	4	1	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	2	1	no	—
179	C₄×D₄₇	—	2	1	no	—
180	C₄×D₄₇	—	2	1	no	—
181	C₄×D₄₇	—	2	1	no	—
182	C₄×D₄₇	—	2	2	no	—
183	C₄×D₄₇	—	2	2	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	C₄×D₄₇	—	4	1	no	—
187	C₄×D₄₇	—	4	1	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₈×C₄₇	—	2	4	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₄₇⋊C₈	—	2	4	no	—
195	C₄₇⋊C₈	—	4	1	no	—
196	C₄₇⋊C₈	—	4	1	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	#17823	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂×D₄₇	—	2	1	no	—
204	C₂×D₄₇	—	2	1	no	—
205	C₂×D₄₇	—	2	1	no	—
206	C₂×D₄₇	—	2	1	no	—
207	C₂×D₄₇	—	2	1	no	—
208	C₂×D₄₇	—	2	1	no	—
209	C₂×D₄₇	—	4	4	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	#568	1	2	yes	—
215	C₄×C₄₇	#575	1	1	yes	characteristic
216	C₄×C₄₇	#575	1	1	yes	characteristic
217	Dic₄₇	—	2	1	no	—
218	Dic₄₇	—	2	1	no	—
219	Dic₄₇	—	2	1	no	—
220	Dic₄₇	—	2	1	no	—
221	Dic₄₇	—	2	1	no	—
222	Dic₄₇	#430	1	2	yes	—
223	#2920	—	47	1	no	—
224	#2920	—	47	1	no	—
225	#2920	—	47	1	no	—
226	#1574	—	47	2	no	—
227	#1574	—	47	2	no	—
228	#1572	—	47	2	no	—
229	#1572	—	47	2	no	—
230	#1569	—	47	1	no	—
231	#1569	—	47	1	no	—
232	#1569	—	47	1	no	—
233	#1569	D₄₇	1	1	yes	characteristic, complemented
234	C₂×C₄₇	—	4	1	no	—
235	C₂×C₄₇	#2905	1	1	yes	characteristic
236	C₂×C₄₇	#2911	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
238	D₄₇	—	4	1	no	—
239	D₄₇	—	4	1	no	—
240	C₂²×C₄²	—	47	1	no	—
241	#432	—	47	2	no	—
242	#432	—	47	2	no	—
243	#432	—	47	1	no	—
244	#432	—	47	2	no	—
245	#432	—	94	1	no	—
246	#432	—	94	1	no	—
247	#432	C₂×D₄₇	1	1	yes	characteristic
248	#431	—	47	2	no	—
249	#431	—	47	2	no	—
250	#431	—	47	1	no	—
251	#431	—	47	1	no	—
252	#431	—	47	2	no	—
253	#431	—	94	1	no	—
254	#431	—	94	1	no	—
255	#423	—	47	2	no	—
256	#423	—	47	1	no	—
257	#423	—	47	1	no	—
258	#423	—	47	1	no	—
259	#423	C₂×D₄₇	1	1	yes	characteristic
260	#407	—	47	2	no	—
261	#407	—	94	1	no	—
262	#407	—	94	1	no	—
263	C₄×M₁₆	—	47	1	no	—
264	C₄×M₁₆	—	94	1	no	—
265	C₄×M₁₆	—	94	1	no	—
266	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
267	#335	—	47	2	no	—
268	#335	—	47	2	no	—
269	#335	—	47	2	no	—
270	#335	C₂×D₄₇	1	2	yes	complemented
271	#334	—	47	2	no	—
272	#334	—	47	2	no	—
273	#334	—	47	2	no	—
274	#334	C₂×D₄₇	1	2	yes	complemented
275	C₄₇	#17823	1	1	yes	characteristic, complemented, Sylow
276	C₂³×C₄	—	47	1	no	—
277	C₂³×C₄	—	47	1	no	—
278	C₂³×C₄	—	47	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	47	2	no	—
281	C₂×M₁₆	—	94	1	no	—
282	C₂×M₁₆	—	94	1	no	—
283	C₂×M₁₆	—	94	1	no	—
284	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	—	47	1	no	—
290	C₂×C₄²	—	47	1	no	—
291	C₂×C₄²	—	47	1	no	—
292	C₂×C₄²	—	47	1	no	—
293	C₂×C₄²	—	47	1	no	—
294	C₂×C₄²	—	47	1	no	—
295	C₂×C₄²	—	47	1	no	—
296	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	47	4	no	—
299	C₄⋊C₈	—	47	4	no	—
300	C₄⋊C₈	—	47	1	no	—
301	C₄⋊C₈	—	47	2	no	—
302	C₄⋊C₈	—	47	1	no	—
303	C₄⋊C₈	—	94	1	no	—
304	C₄⋊C₈	—	94	1	no	—
305	C₄⋊C₈	—	94	1	no	—
306	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
308	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	47	4	no	—
311	C₂²⋊C₈	—	47	4	no	—
312	C₂²⋊C₈	—	94	1	no	—
313	C₂²⋊C₈	—	94	1	no	—
314	C₂²⋊C₈	—	94	2	no	—
315	C₂²⋊C₈	—	94	2	no	—
316	C₂²⋊C₈	—	94	1	no	—
317	#97	—	2	1	no	—
318	#97	—	47	2	no	—
319	#97	—	94	2	no	—
320	#97	—	94	1	no	—
321	#97	C₄×D₄₇	1	2	yes	—
322	C₄×C₈	—	47	2	no	—
323	C₄×C₈	—	94	1	no	—
324	C₄×C₈	—	94	1	no	—
325	C₄×C₈	—	94	2	no	—
326	C₄×C₈	C₂²×D₄₇	1	2	yes	—
327	C₂⁴	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	47	1	no	—
331	C₂²×C₄	—	47	1	no	—
332	C₂²×C₄	—	47	1	no	—
333	C₂²×C₄	—	47	1	no	—
334	C₂²×C₄	—	47	1	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	47	1	no	—
337	C₂²×C₄	—	47	1	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	1	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	188	2	no	—
344	C₂²×C₄	—	188	1	no	—
345	C₂²×C₄	—	188	1	no	—
346	C₂²×C₄	—	188	2	no	—
347	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
350	M₁₆	—	4	2	no	—
351	M₁₆	—	4	2	no	—
352	M₁₆	—	188	2	no	—
353	M₁₆	—	188	2	no	—
354	M₁₆	—	188	2	no	—
355	M₁₆	—	188	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	47	4	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
364	C₄²	—	47	1	no	—
365	C₄²	—	47	1	no	—
366	C₄²	—	47	1	no	—
367	C₄²	—	47	1	no	—
368	C₄²	—	47	1	no	—
369	C₄²	—	47	1	no	—
370	C₄²	—	47	1	no	—
371	C₄²	—	47	1	no	—
372	C₄²	—	47	1	no	—
373	C₄²	—	47	1	no	—
374	C₄²	—	47	1	no	—
375	C₄²	—	47	1	no	—
376	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
377	C₄²	D₄×D₄₇	1	1	yes	characteristic
378	C₄²	Q₈×D₄₇	1	1	yes	characteristic
379	C₄²	C₂³×D₄₇	1	1	yes	characteristic
380	C₂³	—	47	1	no	—
381	C₂³	—	47	1	no	—
382	C₂³	—	188	1	no	—
383	C₂³	—	188	1	no	—
384	C₂³	—	188	1	no	—
385	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	47	1	no	—
391	C₂×C₄	—	47	1	no	—
392	C₂×C₄	—	47	1	no	—
393	C₂×C₄	—	47	1	no	—
394	C₂×C₄	—	47	1	no	—
395	C₂×C₄	—	47	1	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	94	2	no	—
399	C₂×C₄	—	94	2	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	—	188	1	no	—
413	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	94	4	no	—
424	C₈	—	188	1	no	—
425	C₈	—	188	1	no	—
426	C₈	—	188	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	94	1	no	—
431	C₂²	—	94	1	no	—
432	C₂²	—	94	1	no	—
433	C₂²	—	94	1	no	—
434	C₂²	—	94	1	no	—
435	C₂²	—	94	1	no	—
436	C₂²	—	188	4	no	—
437	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	47	2	no	—
443	C₄	—	94	1	no	—
444	C₄	—	94	1	no	—
445	C₄	—	94	1	no	—
446	C₄	—	94	1	no	—
447	C₄	—	94	1	no	—
448	C₄	#15689889	1	2	yes	—
449	C₄	#15689919	1	1	yes	characteristic
450	C₄	#15689922	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	188	1	no	—
453	C₂	—	188	1	no	—
454	C₂	#20251950	1	1	yes	characteristic
455	C₂	#20251975	1	1	yes	characteristic
456	C₂	#430×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×#1569	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1569	D₄₇
hypocenter	C₄₇	#17823
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #20242178	C₂	semidirect
5. #20242175	C₂	semidirect
6. #20242167	C₂	semidirect
7. #20242165	C₂	semidirect
8. #20242156	C₂	semidirect
9. #20242155	C₂	semidirect
10. #20242153	C₂	semidirect
11. C₄₇×#1569	C₂	semidirect
36. #15688876	C₂²	semidirect
37. #15688875	C₂²	semidirect
38. #15688875	C₂²	semidirect
39. #15688874	C₂²	semidirect
40. #15688873	C₂²	semidirect
41. #15688873	C₂²	semidirect
45. C₄₇×#335	C₂²	semidirect
46. C₄₇×#334	C₂²	semidirect
233. #1569	D₄₇	semidirect
270. #335	C₂×D₄₇	semidirect
274. #334	C₂×D₄₇	semidirect
275. C₄₇	#17823	semidirect

Maximal subgroups

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

subgroup	index
#20252020	2
#20252019	2
#20252018	2
#20242178	2
#20242175	2
#20242167	2
#20242165	2
#20242156	2
#20242155	2
#20242153	2
C₄₇×#1569	2
#17823	47