Subgroups — #26220240

Order 12032.

1498 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	2	yes	maximal, complemented
3	#20251833	C₂	1	2	yes	maximal, complemented
4	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244282	C₂	1	4	yes	maximal, complemented
6	#20244277	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#575	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	2	yes	—
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
11	#15689172	—	2	4	no	—
12	C₂×#13093960	C₂²	1	4	yes	complemented
13	C₂×#13093951	—	2	8	no	—
14	C₂×#13093951	C₂²	1	4	yes	complemented
15	C₂×#13093951	C₂²	1	4	yes	complemented
16	#15689090	—	2	4	no	—
17	#15689090	C₂²	1	8	yes	complemented
18	#15689087	—	2	4	no	—
19	M₁₆×Dic₄₇	—	2	4	no	—
20	C₂×#13093934	C₂²	1	2	yes	complemented
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
22	C₂²×#41×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#575	—	2	4	no	—
24	C₄₇×#575	—	2	4	no	—
25	C₂×#137×C₄₇	C₄	1	4	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₄₇	C₄	1	4	yes	complemented
27	C₂×#135×C₄₇	C₂²	1	4	yes	—
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×Dic₄₇	—	2	1	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	—	2	4	no	—
35	C₂×#10625329	D₄	1	4	yes	—
36	C₂×#10625329	C₂³	1	4	yes	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	1	no	—
41	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
42	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
44	#13093960	—	2	8	no	—
45	#13093951	—	2	8	no	—
46	#13093951	—	2	8	no	—
47	C₂²⋊(C₄₇⋊C₈)	—	2	16	no	—
48	#13093934	—	2	4	no	—
49	C₈×Dic₄₇	—	2	4	no	—
50	C₂×#41×C₄₇	—	2	2	no	—
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	—	2	4	no	—
53	C₂×#41×C₄₇	—	2	4	no	—
54	C₂×#41×C₄₇	—	2	4	no	—
55	C₂×#41×C₄₇	—	2	4	no	—
56	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×#41×C₄₇	C₂³	1	4	yes	—
58	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
59	C₂²×D₄×C₄₇	—	2	2	no	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	—	2	2	no	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	#137×C₄₇	—	2	16	no	—
64	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
65	#135×C₄₇	—	2	8	no	—
66	#135×C₄₇	—	2	8	no	—
67	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
68	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
69	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
70	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
72	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	#41	1	1	yes	characteristic
76	#41×C₄₇	—	2	8	no	—
77	#41×C₄₇	—	2	8	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	4	4	no	—
83	#41×C₄₇	—	4	4	no	—
84	#41×C₄₇	—	4	4	no	—
85	#41×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	4	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	4	4	no	—
96	C₂×D₄×C₄₇	—	4	4	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	4	4	no	—
102	C₂²×C₄×C₄₇	—	4	4	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	1	no	—
112	C₂²×Dic₄₇	—	2	4	no	—
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	4	4	no	—
115	Q₁₆×C₄₇	—	2	8	no	—
116	SD₁₆×C₄₇	—	2	16	no	—
117	D₈×C₄₇	—	2	8	no	—
118	M₁₆×C₄₇	C₂²⋊C₄	1	16	yes	—
119	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
120	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	1	no	—
125	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
126	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
127	#10625329	—	2	8	no	—
128	#10625329	—	2	4	no	—
129	#10625329	—	2	4	no	—
130	#10625329	—	4	4	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	4	4	no	—
135	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	4	no	—
139	C₂³×C₄₇	—	8	4	no	—
140	C₂³×C₄₇	C₄×D₄	1	2	yes	—
141	C₂³×C₄₇	#121	1	2	yes	—
142	C₂³×C₄₇	#124	1	2	yes	—
143	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	4	no	—
145	Q₈×C₄₇	—	2	4	no	—
146	Q₈×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	2	4	no	—
149	D₄×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	4	4	no	—
151	D₄×C₄₇	—	4	8	no	—
152	D₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	—	4	8	no	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	#121	1	4	yes	—
162	C₂×C₄×C₄₇	#121	1	2	yes	—
163	C₂×C₄×C₄₇	#124	1	2	yes	—
164	C₂×C₄×C₄₇	#127	1	4	yes	—
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×Dic₄₇	—	2	4	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	4	8	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
177	C₄₇⋊C₈	—	2	4	no	—
178	C₄₇⋊C₈	—	4	4	no	—
179	#21241	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	4	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	8	no	—
185	C₂²×C₄₇	—	4	4	no	—
186	C₂²×C₄₇	—	8	8	no	—
187	C₂²×C₄₇	#390	1	4	yes	—
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	#390	1	4	yes	—
193	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
194	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
196	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	4	2	no	—
199	C₂×#575	D₄₇	1	1	yes	characteristic
200	C₂×#430	—	47	1	no	—
201	C₂²×#104	—	47	2	no	—
202	#2879	—	47	2	no	—
203	C₂×C₄×M₁₆	—	47	1	no	—
204	#1975	—	47	4	no	—
205	#1974	—	47	4	no	—
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	—	2	4	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	8	4	no	—
210	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
211	C₂×C₄₇	#2956	1	2	yes	—
212	C₂²×#41	C₂×D₄₇	1	2	yes	—
213	#575	—	2	4	no	—
214	#575	—	2	4	no	—
215	C₂×#137	Dic₄₇	1	4	yes	complemented
216	C₂×AGL(1,ℤ/8)	Dic₄₇	1	4	yes	complemented
217	C₂×#135	C₂×D₄₇	1	4	yes	—
218	C₂²×M₁₆	—	47	1	no	—
219	C₂²×M₁₆	—	47	2	no	—
220	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×C₄²	—	47	1	no	—
222	#430	—	94	4	no	—
223	C₂×#108	—	47	4	no	—
224	C₂×#104	—	47	4	no	—
225	C₂×#104	—	47	4	no	—
226	C₂×#104	—	94	8	no	—
227	#408	—	47	8	no	—
228	#408	—	94	4	no	—
229	#407	—	94	4	no	—
230	C₄×M₁₆	—	94	4	no	—
231	C₂×#97	—	47	2	no	—
232	C₂×C₄×C₈	—	47	2	no	—
233	C₄₇	#21241	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	4	no	—
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	C₂×Dic₄₇	1	4	yes	—
241	C₂×#41	C₂²×D₄₇	1	4	yes	—
242	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	94	1	no	—
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	#137	—	2	16	no	—
249	AGL(1,ℤ/8)	—	2	16	no	—
250	#135	—	2	8	no	—
251	#135	—	2	8	no	—
252	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
253	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
254	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
255	C₂×M₁₆	—	47	4	no	—
256	C₂×M₁₆	—	47	4	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	4	no	—
261	C₂×M₁₆	—	94	4	no	—
262	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
263	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
264	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
265	C₂²×C₈	—	47	2	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
268	C₂×C₄²	—	47	4	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	94	1	no	—
272	C₂×C₄²	—	94	2	no	—
273	#108	—	94	8	no	—
274	#104	—	94	8	no	—
275	#104	—	94	8	no	—
276	C₂²⋊C₈	—	94	16	no	—
277	#97	—	94	4	no	—
278	C₄×C₈	—	94	4	no	—
279	C₂⁴	—	2	2	no	—
280	C₂⁴	#10625352	1	1	yes	characteristic
281	#41	—	2	8	no	—
282	#41	—	2	8	no	—
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	4	4	no	—
288	#41	—	4	4	no	—
289	#41	—	4	4	no	—
290	#41	—	4	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	94	1	no	—
309	C₂²×C₄	—	94	4	no	—
310	C₂²×C₄	—	94	1	no	—
311	C₂²×C₄	—	188	4	no	—
312	C₂²×C₄	D₄×D₄₇	1	2	yes	—
313	C₂²×C₄	D₄×D₄₇	1	2	yes	—
314	C₂²×C₄	#10625352	1	1	yes	characteristic
315	C₂²×C₄	#10625352	1	2	yes	—
316	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
317	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
319	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
320	Q₁₆	—	2	8	no	—
321	SD₁₆	—	2	16	no	—
322	D₈	—	2	8	no	—
323	M₁₆	—	94	8	no	—
324	M₁₆	—	94	4	no	—
325	M₁₆	—	94	4	no	—
326	M₁₆	—	188	4	no	—
327	M₁₆	C₂²⋊Dic₄₇	1	16	yes	—
328	C₂×C₈	—	47	4	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	4	no	—
332	C₂×C₈	—	188	4	no	—
333	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
334	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
335	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
336	C₄²	—	47	2	no	—
337	C₄²	—	47	2	no	—
338	C₄²	—	94	4	no	—
339	C₄²	—	94	1	no	—
340	C₄²	—	94	1	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	8	4	no	—
345	C₂³	D₄×Dic₄₇	1	2	yes	—
346	C₂³	#13093995	1	2	yes	—
347	C₂³	#13094011	1	2	yes	—
348	C₂³	C₂×#10625352	1	1	yes	characteristic
349	Q₈	—	2	4	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	4	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	4	8	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	188	8	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
369	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
370	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
371	C₂×C₄	#13093995	1	2	yes	—
372	C₂×C₄	#13093995	1	4	yes	—
373	C₂×C₄	#13094011	1	2	yes	—
374	C₂×C₄	#13094020	1	4	yes	—
375	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
381	C₈	—	94	4	no	—
382	C₈	—	188	4	no	—
383	C₈	C₂×C₂²⋊Dic₄₇	1	8	yes	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	8	8	no	—
391	C₂²	#15689026	1	4	yes	—
392	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
393	C₂²	C₂×#13093995	1	1	yes	characteristic
394	C₂²	C₂×#13094011	1	1	yes	characteristic
395	C₄	—	4	4	no	—
396	C₄	—	94	4	no	—
397	C₄	—	188	2	no	—
398	C₄	#15689026	1	4	yes	—
399	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
400	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
401	C₄	C₂×#13093995	1	1	yes	characteristic
402	C₄	C₂×#13094020	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	2	1	no	—
406	C₂	—	8	4	no	—
407	C₂	C₂×#15689026	1	1	yes	characteristic
408	C₂	#20252298	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#575	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#575	D₄₇
hypocenter	C₄₇	#21241
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#575

Complements

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

N	H ≅ G/N	type
1. C₂×#15689172	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. #20251833	C₂	semidirect
4. C₂×M₁₆×Dic₄₇	C₂	semidirect
5. #20244282	C₂	semidirect
6. #20244277	C₂	semidirect
12. C₂×#13093960	C₂²	semidirect
14. C₂×#13093951	C₂²	semidirect
15. C₂×#13093951	C₂²	semidirect
17. #15689090	C₂²	semidirect
20. C₂×#13093934	C₂²	semidirect
21. C₂×C₈×Dic₄₇	C₂²	semidirect
25. C₂×#137×C₄₇	C₄	semidirect
26. C₂×AGL(1,ℤ/8)×C₄₇	C₄	semidirect
67. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
68. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
69. C₂×D₈×C₄₇	C₂×C₄	semidirect
215. C₂×#137	Dic₄₇	semidirect
216. C₂×AGL(1,ℤ/8)	Dic₄₇	semidirect
233. C₄₇	#21241	semidirect
252. C₂×Q₁₆	C₂×Dic₄₇	semidirect
253. C₂×SD₁₆	C₂×Dic₄₇	semidirect
254. C₂×D₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689172	2
C₂²×#13093951	2
#20251833	2
C₂×M₁₆×Dic₄₇	2
#20244282	2
#20244277	2
C₂×C₄₇×#575	2
#21241	47