Subgroups — C₂×#20244147 #26219721

Order 12032.

1230 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093958	C₂	1	2	yes	maximal
2	C₂×#15688993	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244147	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688886	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
8	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
9	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	—	2	1	no	—
13	C₂×#13093958	—	2	8	no	—
14	C₂×#13093958	C₂²	1	8	yes	—
15	#15688993	—	2	2	no	—
16	#15688993	C₂²	1	4	yes	—
17	C₄×C₄⋊Dic₄₇	—	2	2	no	—
18	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
19	C₂×C₄₇⋊#95	—	2	1	no	—
20	#15688886	C₂²	1	8	yes	—
21	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₄	1	8	yes	complemented
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
25	C₂³×Dic₄₇	—	2	1	no	—
26	C₂³×Dic₄₇	—	2	1	no	—
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	1	no	—
29	C₂×C₄⋊Dic₄₇	—	2	1	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	2	4	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	4	no	—
37	C₂×C₄⋊Dic₄₇	—	4	4	no	—
38	C₂×C₄⋊Dic₄₇	—	4	4	no	—
39	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
40	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
41	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
42	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₂×C₄×Dic₄₇	—	2	4	no	—
45	C₂×C₄×Dic₄₇	—	4	4	no	—
46	#13093958	—	2	16	no	—
47	C₄₇⋊#95	—	2	4	no	—
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	—	2	4	no	—
52	C₂²×C₈×C₄₇	—	2	4	no	—
53	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
54	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄²×C₄₇	D₄	1	2	yes	—
57	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
58	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
59	C₄⋊C₈×C₄₇	C₂×C₄	1	16	yes	complemented
60	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
64	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
65	C₂²×C₄×C₄₇	D₈	1	4	yes	—
66	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
67	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
74	C₂²×C₄×C₄₇	#41	1	2	yes	—
75	C₂²×C₄×C₄₇	#41	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	4	no	—
78	C₂²×Dic₄₇	—	2	4	no	—
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	2	2	no	—
81	C₂²×Dic₄₇	—	2	4	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	4	no	—
87	C₂²×Dic₄₇	—	4	4	no	—
88	C₂²×Dic₄₇	—	4	4	no	—
89	C₂×C₈×C₄₇	—	2	16	no	—
90	C₂×C₈×C₄₇	—	2	4	no	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
93	C₄²×C₄₇	C₄⋊C₄	1	8	yes	—
94	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
95	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
96	C₄⋊Dic₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	2	4	no	—
98	C₄⋊Dic₄₇	—	2	2	no	—
99	C₄⋊Dic₄₇	—	2	2	no	—
100	C₄⋊Dic₄₇	—	2	4	no	—
101	C₄⋊Dic₄₇	—	2	4	no	—
102	C₄⋊Dic₄₇	—	4	8	no	—
103	C₄⋊Dic₄₇	—	4	4	no	—
104	C₄⋊Dic₄₇	—	4	8	no	—
105	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
106	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
107	C₄×Dic₄₇	—	4	8	no	—
108	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
109	C₂³×C₄₇	#121	1	2	yes	—
110	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
111	C₂³×C₄₇	C₂×D₈	1	2	yes	—
112	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
113	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
114	C₂³×C₄₇	#137	1	2	yes	—
115	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
116	C₂×C₄×C₄₇	—	2	2	no	—
117	C₂×C₄×C₄₇	—	2	2	no	—
118	C₂×C₄×C₄₇	—	2	8	no	—
119	C₂×C₄×C₄₇	#107	1	16	yes	complemented
120	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
121	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
123	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
124	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
125	C₂×C₄×C₄₇	#121	1	2	yes	—
126	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
127	C₂×C₄×C₄₇	#125	1	4	yes	—
128	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
129	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
130	C₂×C₄×C₄₇	C₂×Q₁₆	1	4	yes	—
131	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
137	C₂×Dic₄₇	—	2	4	no	—
138	C₂×Dic₄₇	—	2	4	no	—
139	C₂×Dic₄₇	—	4	2	no	—
140	C₂×Dic₄₇	—	4	2	no	—
141	C₂×Dic₄₇	—	4	2	no	—
142	C₂×Dic₄₇	—	4	2	no	—
143	C₂×Dic₄₇	—	4	8	no	—
144	C₂×Dic₄₇	—	4	8	no	—
145	C₂×Dic₄₇	—	4	4	no	—
146	C₂×Dic₄₇	—	4	4	no	—
147	C₂×Dic₄₇	—	4	4	no	—
148	C₂×Dic₄₇	—	8	8	no	—
149	C₈×C₄₇	—	2	8	no	—
150	C₂×#1947	—	47	1	no	maximal, Sylow
151	C₂²×C₄₇	#389	1	4	yes	—
152	C₂²×C₄₇	C₂×#107	1	4	yes	—
153	C₂²×C₄₇	#428	1	4	yes	—
154	C₂²×C₄₇	#459	1	4	yes	—
155	C₂²×C₄₇	#462	1	4	yes	—
156	C₂²×C₄₇	#474	1	4	yes	—
157	C₂²×C₄₇	#477	1	4	yes	—
158	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
161	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
162	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
165	C₄×C₄₇	—	2	4	no	—
166	C₄×C₄₇	#389	1	4	yes	—
167	C₄×C₄₇	C₂×#107	1	8	yes	complemented
168	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
170	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
171	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
172	Dic₄₇	—	4	4	no	—
173	Dic₄₇	—	4	4	no	—
174	Dic₄₇	—	8	4	no	—
175	C₂²×#107	—	47	2	no	—
176	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
177	C₂×#384	—	47	1	no	—
178	C₂×C₄×C₄⋊C₄	—	47	1	no	—
179	#1947	—	47	8	no	—
180	C₂×#340	—	47	2	no	—
181	C₂×C₄₇	#1947	1	8	yes	complemented
182	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
183	C₂×C₄₇	C₂²×#107	1	1	yes	characteristic
184	C₂×C₄₇	C₂×#428	1	1	yes	characteristic
185	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
186	C₂×C₄₇	C₂×#462	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#474	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#477	1	1	yes	characteristic
189	C₂³×C₈	C₂×D₄₇	1	2	yes	—
190	C₂²×C₄⋊C₄	—	47	1	no	—
191	C₂²×C₄⋊C₄	—	47	1	no	—
192	C₂²×C₄⋊C₄	—	47	2	no	—
193	C₂²×C₄⋊C₄	—	94	1	no	—
194	C₂²×C₄⋊C₄	—	94	1	no	—
195	C₂²×C₄²	—	94	1	no	—
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₂×#107	—	47	8	no	—
198	C₂×#107	—	94	8	no	—
199	C₂×C₄⋊C₈	Dic₄₇	1	8	yes	complemented
200	C₂×C₄⋊C₈	C₂×D₄₇	1	4	yes	—
201	#384	—	47	4	no	—
202	#384	—	94	2	no	—
203	C₄×C₄⋊C₄	—	47	4	no	—
204	C₄×C₄⋊C₄	—	94	2	no	—
205	C₂×#95	—	94	1	no	—
206	#340	—	47	8	no	—
207	C₄₇	C₂×#1947	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₄	—	94	1	no	—
209	C₂³×C₄	—	94	1	no	—
210	C₂³×C₄	—	94	2	no	—
211	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
212	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
213	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	—	2	4	no	—
216	C₂²×C₈	C₂×Dic₄₇	1	8	yes	—
217	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
218	C₂×C₄⋊C₄	—	47	4	no	—
219	C₂×C₄⋊C₄	—	47	4	no	—
220	C₂×C₄⋊C₄	—	47	2	no	—
221	C₂×C₄⋊C₄	—	47	2	no	—
222	C₂×C₄⋊C₄	—	47	4	no	—
223	C₂×C₄⋊C₄	—	94	1	no	—
224	C₂×C₄⋊C₄	—	94	1	no	—
225	C₂×C₄⋊C₄	—	94	2	no	—
226	C₂×C₄⋊C₄	—	94	2	no	—
227	C₂×C₄⋊C₄	—	94	4	no	—
228	C₂×C₄⋊C₄	—	94	4	no	—
229	C₂×C₄⋊C₄	—	94	2	no	—
230	C₂×C₄⋊C₄	—	94	4	no	—
231	C₂×C₄⋊C₄	—	94	4	no	—
232	C₂×C₄⋊C₄	—	188	4	no	—
233	C₂×C₄⋊C₄	—	188	4	no	—
234	C₂×C₄²	—	94	4	no	—
235	C₂×C₄²	—	188	4	no	—
236	C₂×C₄²	Dic₉₄	1	4	yes	—
237	C₂×C₄²	D₁₈₈	1	2	yes	—
238	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
239	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
240	#107	—	94	16	no	—
241	C₄⋊C₈	C₂×Dic₄₇	1	16	yes	complemented
242	#95	—	94	4	no	—
243	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	94	4	no	—
247	C₂²×C₄	—	94	4	no	—
248	C₂²×C₄	—	94	2	no	—
249	C₂²×C₄	—	94	2	no	—
250	C₂²×C₄	—	94	4	no	—
251	C₂²×C₄	—	188	4	no	—
252	C₂²×C₄	—	188	4	no	—
253	C₂²×C₄	—	188	4	no	—
254	C₂²×C₄	—	188	2	no	—
255	C₂²×C₄	—	188	2	no	—
256	C₂²×C₄	—	188	2	no	—
257	C₂²×C₄	—	188	2	no	—
258	C₂²×C₄	D₃₇₆	1	4	yes	—
259	C₂²×C₄	Dic₁₈₈	1	4	yes	—
260	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
261	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
262	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
263	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
264	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
266	C₂²×C₄	D₄×D₄₇	1	2	yes	—
267	C₂²×C₄	#10625352	1	2	yes	—
268	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
269	C₂²×C₄	#10625354	1	2	yes	—
270	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
271	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
272	C₂×C₈	—	2	16	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
276	C₄⋊C₄	—	47	4	no	—
277	C₄⋊C₄	—	47	4	no	—
278	C₄⋊C₄	—	94	4	no	—
279	C₄⋊C₄	—	94	4	no	—
280	C₄⋊C₄	—	94	2	no	—
281	C₄⋊C₄	—	94	2	no	—
282	C₄⋊C₄	—	94	4	no	—
283	C₄⋊C₄	—	94	4	no	—
284	C₄⋊C₄	—	188	8	no	—
285	C₄⋊C₄	—	188	4	no	—
286	C₄⋊C₄	—	188	8	no	—
287	C₄²	—	188	8	no	—
288	C₄²	C₄⋊Dic₄₇	1	8	yes	—
289	C₄²	C₂×Dic₉₄	1	4	yes	—
290	C₄²	C₂²×Dic₄₇	1	4	yes	—
291	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
292	C₂³	#13093999	1	2	yes	—
293	C₂³	#13094004	1	2	yes	—
294	C₂³	C₂×D₃₇₆	1	2	yes	—
295	C₂³	C₂×Dic₁₈₈	1	2	yes	—
296	C₂³	#13094052	1	2	yes	—
297	C₂³	#13094057	1	2	yes	—
298	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	94	4	no	—
303	C₂×C₄	—	94	4	no	—
304	C₂×C₄	—	376	8	no	—
305	C₂×C₄	—	188	4	no	—
306	C₂×C₄	—	188	4	no	—
307	C₂×C₄	—	188	4	no	—
308	C₂×C₄	—	188	8	no	—
309	C₂×C₄	—	188	2	no	—
310	C₂×C₄	—	188	2	no	—
311	C₂×C₄	—	188	2	no	—
312	C₂×C₄	—	188	8	no	—
313	C₂×C₄	—	188	2	no	—
314	C₂×C₄	#13093958	1	16	yes	complemented
315	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
316	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
318	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
319	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
320	C₂×C₄	#13093999	1	2	yes	—
321	C₂×C₄	#13094004	1	2	yes	—
322	C₂×C₄	#13094015	1	4	yes	—
323	C₂×C₄	#13094023	1	4	yes	—
324	C₂×C₄	C₂×D₃₇₆	1	4	yes	—
325	C₂×C₄	C₂×Dic₁₈₈	1	4	yes	—
326	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
330	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
331	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
332	C₈	—	2	8	no	—
333	C₂²	#15689022	1	4	yes	—
334	C₂²	C₂×#13093958	1	4	yes	—
335	C₂²	#15689165	1	4	yes	—
336	C₂²	#15689319	1	4	yes	—
337	C₂²	#15689334	1	4	yes	—
338	C₂²	#15689404	1	4	yes	—
339	C₂²	#15689419	1	4	yes	—
340	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
341	C₂²	C₂×#13093999	1	1	yes	characteristic
342	C₂²	C₂×#13094004	1	1	yes	characteristic
343	C₂²	C₂²×D₃₇₆	1	1	yes	characteristic
344	C₂²	C₂²×Dic₁₈₈	1	1	yes	characteristic
345	C₂²	C₂×#13094052	1	1	yes	characteristic
346	C₂²	C₂×#13094057	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	376	4	no	—
349	C₄	—	188	4	no	—
350	C₄	—	188	4	no	—
351	C₄	#15689022	1	4	yes	—
352	C₄	C₂×#13093958	1	8	yes	complemented
353	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
354	C₄	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
355	C₄	C₂×#13094015	1	1	yes	characteristic
356	C₄	C₂×#13094023	1	1	yes	characteristic
357	C₂	#20244147	1	8	yes	direct product factor
358	C₂	C₂×#15689022	1	1	yes	characteristic
359	C₂	C₂²×#13093958	1	1	yes	characteristic
360	C₂	C₂×#15689165	1	1	yes	characteristic
361	C₂	C₂×#15689319	1	1	yes	characteristic
362	C₂	C₂×#15689334	1	1	yes	characteristic
363	C₂	C₂×#15689404	1	1	yes	characteristic
364	C₂	C₂×#15689419	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	C₂×#1947
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #20244147	C₂	direct (N × H)
23. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
59. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
119. C₂×C₄×C₄₇	#107	semidirect
167. C₄×C₄₇	C₂×#107	semidirect
181. C₂×C₄₇	#1947	semidirect
199. C₂×C₄⋊C₈	Dic₄₇	semidirect
207. C₄₇	C₂×#1947	semidirect
241. C₄⋊C₈	C₂×Dic₄₇	semidirect
314. C₂×C₄	#13093958	semidirect
352. C₄	C₂×#13093958	semidirect
357. C₂	#20244147	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13093958	2
C₂×#15688993	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244147	2
C₂×#15688886	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×#1947	47

Subgroups — C2×#20244147 #26219721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244147 #26219721