Subgroups — C₄×C₄⋊C₄×Dic₄₇ #26137356

Order 12032.

2478 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×Dic₄₇	C₂	1	4	yes	maximal
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×Dic₄₇	C₂	1	2	yes	maximal
4	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄×C₄₇⋊#95	C₂	1	2	yes	maximal
6	#95×Dic₄₇	C₂	1	4	yes	maximal
7	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
10	C₂²×C₄×Dic₄₇	C₂²	1	8	yes	—
11	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×Dic₄₇	C₄	1	32	yes	direct product factor
16	C₄×C₄⋊Dic₄₇	C₄	1	8	yes	complemented
17	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
18	C₂×C₄₇⋊#95	C₂²	1	8	yes	—
19	C₄²×Dic₄₇	—	2	8	no	—
20	C₄²×Dic₄₇	C₄	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₄₇	C₄	1	8	yes	complemented
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂³×Dic₄₇	C₂³	1	2	yes	—
27	C₂³×Dic₄₇	C₂³	1	4	yes	—
28	C₂³×Dic₄₇	C₂³	1	2	yes	—
29	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	16	yes	—
31	C₂×C₄×Dic₄₇	—	2	4	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	4	no	—
35	C₂×C₄×Dic₄₇	—	2	16	no	—
36	C₂×C₄×Dic₄₇	—	2	8	no	—
37	C₂×C₄×Dic₄₇	—	2	16	no	—
38	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
39	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
40	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	32	yes	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	16	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
46	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
47	C₄₇⋊#95	C₂×C₄	1	8	yes	—
48	C₄₇⋊#95	C₂×C₄	1	32	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
61	#95×C₄₇	C₂×C₄	1	8	yes	—
62	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	—	2	4	no	—
64	C₂²×C₄×C₄₇	—	2	4	no	—
65	C₂²×C₄×C₄₇	—	2	4	no	—
66	C₂²×C₄×C₄₇	—	2	8	no	—
67	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
70	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
74	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×Dic₄₇	—	2	4	no	—
84	C₂²×Dic₄₇	—	2	4	no	—
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	8	no	—
88	C₂²×Dic₄₇	—	2	4	no	—
89	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
90	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
91	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
92	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
95	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
96	C₂²×Dic₄₇	C₂×Q₈	1	4	yes	—
97	C₂²×Dic₄₇	#41	1	8	yes	—
98	C₄⋊C₄×C₄₇	C₄²	1	32	yes	complemented
99	C₄²×C₄₇	—	2	16	no	—
100	C₄²×C₄₇	C₄²	1	16	yes	complemented
101	C₄⋊Dic₄₇	C₄²	1	32	yes	complemented
102	C₄×Dic₄₇	—	2	8	no	—
103	C₄×Dic₄₇	—	2	16	no	—
104	C₄×Dic₄₇	—	2	16	no	—
105	C₄×Dic₄₇	—	2	64	no	—
106	C₄×Dic₄₇	C₄²	1	32	yes	complemented
107	C₄×Dic₄₇	C₄⋊C₄	1	16	yes	direct product factor
108	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
109	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
110	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
111	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
112	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
113	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
114	C₂³×C₄₇	C₂×#41	1	4	yes	—
115	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
116	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
117	C₂×C₄×C₄₇	—	2	4	no	—
118	C₂×C₄×C₄₇	—	2	16	no	—
119	C₂×C₄×C₄₇	—	2	8	no	—
120	C₂×C₄×C₄₇	—	2	16	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	8	no	—
124	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
125	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
126	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
127	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	—
128	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
129	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
130	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
131	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
132	C₂×C₄×C₄₇	#117	1	4	yes	—
133	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
134	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
136	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
137	C₂×Dic₄₇	—	2	4	no	—
138	C₂×Dic₄₇	—	2	4	no	—
139	C₂×Dic₄₇	—	2	16	no	—
140	C₂×Dic₄₇	—	2	8	no	—
141	C₂×Dic₄₇	—	2	8	no	—
142	C₂×Dic₄₇	—	2	8	no	—
143	C₂×Dic₄₇	—	2	8	no	—
144	C₂×Dic₄₇	—	2	16	no	—
145	C₂×Dic₄₇	C₂×C₄²	1	8	yes	—
146	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
147	C₂×Dic₄₇	C₂×C₄²	1	8	yes	—
148	C₂×Dic₄₇	C₂×C₄⋊C₄	1	8	yes	—
149	C₂×Dic₄₇	#117	1	8	yes	—
150	C₂×Dic₄₇	C₄×D₄	1	16	yes	—
151	C₂×Dic₄₇	C₄×Q₈	1	16	yes	—
152	C₄²×C₄⋊C₄	—	47	1	no	maximal, Sylow
153	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
154	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
155	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
156	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
157	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₂²×C₄₇	C₂×#117	1	2	yes	—
159	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
161	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
164	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
166	C₂²×C₄₇	C₄×#41	1	4	yes	—
167	C₂²×C₄₇	C₄×#41	1	2	yes	—
168	C₂²×C₄₇	C₄×#41	1	4	yes	—
169	C₂²×C₄₇	C₄×#41	1	2	yes	—
170	C₄×C₄₇	—	2	4	no	—
171	C₄×C₄₇	—	2	16	no	—
172	C₄×C₄₇	C₄³	1	8	yes	complemented
173	C₄×C₄₇	C₄×C₄⋊C₄	1	8	yes	complemented
174	Dic₄₇	—	2	8	no	—
175	Dic₄₇	—	2	16	no	—
176	Dic₄₇	C₄×C₄⋊C₄	1	16	yes	direct product factor
177	C₂×C₄×C₄⋊C₄	—	47	1	no	—
178	C₂×C₄×C₄⋊C₄	—	47	4	no	—
179	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
180	C₂×C₄³	—	47	1	no	—
181	C₂×C₄³	—	47	2	no	—
182	C₄×#95	—	47	2	no	—
183	C₄×#95	—	47	4	no	—
184	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
185	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	2	yes	—
186	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄₇	C₄×#117	1	2	yes	—
188	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
189	C₂×C₄₇	C₄²×D₄	1	2	yes	—
190	C₂×C₄₇	C₄²×D₄	1	2	yes	—
191	C₂×C₄₇	C₄²×Q₈	1	2	yes	—
192	C₂×C₄₇	C₄²×Q₈	1	2	yes	—
193	C₂²×C₄⋊C₄	—	47	2	no	—
194	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
195	C₂²×C₄²	—	47	2	no	—
196	C₂²×C₄²	—	47	1	no	—
197	C₂²×C₄²	—	47	2	no	—
198	C₂²×C₄²	—	47	8	no	—
199	C₂²×C₄²	—	47	1	no	—
200	C₂²×C₄²	—	47	2	no	—
201	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
202	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
203	C₄×C₄⋊C₄	—	47	32	no	—
204	C₄×C₄⋊C₄	—	47	8	no	—
205	C₄×C₄⋊C₄	Dic₄₇	1	8	yes	direct product factor
206	C₂×#95	—	47	2	no	—
207	C₂×#95	—	47	8	no	—
208	C₂×#95	C₂×D₄₇	1	2	yes	—
209	C₄³	—	47	8	no	—
210	C₄³	—	94	8	no	—
211	C₄₇	C₄²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	—	47	2	no	—
213	C₂³×C₄	—	47	4	no	—
214	C₂³×C₄	—	47	2	no	—
215	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
216	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
219	C₂×C₄⋊C₄	—	47	16	no	—
220	C₂×C₄⋊C₄	—	47	8	no	—
221	C₂×C₄⋊C₄	C₄×D₄₇	1	16	yes	—
222	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
223	C₂×C₄²	—	2	4	no	—
224	C₂×C₄²	—	2	4	no	—
225	C₂×C₄²	—	47	8	no	—
226	C₂×C₄²	—	47	4	no	—
227	C₂×C₄²	—	47	16	no	—
228	C₂×C₄²	—	47	4	no	—
229	C₂×C₄²	—	47	4	no	—
230	C₂×C₄²	—	47	8	no	—
231	C₂×C₄²	—	47	4	no	—
232	C₂×C₄²	—	47	32	no	—
233	C₂×C₄²	—	47	8	no	—
234	C₂×C₄²	—	94	16	no	—
235	C₂×C₄²	—	94	8	no	—
236	C₂×C₄²	—	94	16	no	—
237	C₂×C₄²	—	94	4	no	—
238	C₂×C₄²	—	94	2	no	—
239	C₂×C₄²	—	94	2	no	—
240	C₂×C₄²	—	94	4	no	—
241	C₂×C₄²	C₄×D₄₇	1	4	yes	—
242	C₂×C₄²	C₄×D₄₇	1	4	yes	—
243	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
244	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
245	#95	—	47	32	no	—
246	#95	—	47	8	no	—
247	#95	C₂×Dic₄₇	1	8	yes	—
248	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	47	4	no	—
254	C₂²×C₄	—	47	8	no	—
255	C₂²×C₄	—	47	4	no	—
256	C₂²×C₄	—	47	4	no	—
257	C₂²×C₄	—	47	8	no	—
258	C₂²×C₄	—	47	8	no	—
259	C₂²×C₄	—	47	16	no	—
260	C₂²×C₄	—	47	8	no	—
261	C₂²×C₄	—	47	4	no	—
262	C₂²×C₄	—	94	4	no	—
263	C₂²×C₄	—	94	4	no	—
264	C₂²×C₄	—	94	8	no	—
265	C₂²×C₄	—	94	2	no	—
266	C₂²×C₄	—	94	2	no	—
267	C₂²×C₄	—	94	4	no	—
268	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
269	C₂²×C₄	C₂×C₄×D₄₇	1	16	yes	—
270	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
271	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
272	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
273	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
274	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
275	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
276	C₂²×C₄	D₄×D₄₇	1	2	yes	—
277	C₂²×C₄	#10625352	1	2	yes	—
278	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
279	C₂²×C₄	#10625354	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
284	C₄⋊C₄	—	47	32	no	—
285	C₄⋊C₄	C₄×Dic₄₇	1	32	yes	direct product factor
286	C₄²	—	2	16	no	—
287	C₄²	—	47	32	no	—
288	C₄²	—	47	16	no	—
289	C₄²	—	94	16	no	—
290	C₄²	—	94	64	no	—
291	C₄²	—	94	8	no	—
292	C₄²	—	94	16	no	—
293	C₄²	C₄×Dic₄₇	1	16	yes	complemented
294	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
295	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
296	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
297	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
298	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
299	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
300	C₂³	#41×D₄₇	1	4	yes	—
301	C₂³	C₂×#10625352	1	1	yes	characteristic
302	C₂³	C₂×#10625354	1	1	yes	characteristic
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	16	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	47	8	no	—
311	C₂×C₄	—	47	8	no	—
312	C₂×C₄	—	47	8	no	—
313	C₂×C₄	—	47	16	no	—
314	C₂×C₄	—	47	16	no	—
315	C₂×C₄	—	47	8	no	—
316	C₂×C₄	—	47	16	no	—
317	C₂×C₄	—	94	4	no	—
318	C₂×C₄	—	94	4	no	—
319	C₂×C₄	—	94	16	no	—
320	C₂×C₄	—	94	8	no	—
321	C₂×C₄	—	94	8	no	—
322	C₂×C₄	—	94	8	no	—
323	C₂×C₄	—	94	8	no	—
324	C₂×C₄	—	94	16	no	—
325	C₂×C₄	C₄²×D₄₇	1	8	yes	—
326	C₂×C₄	C₄²×D₄₇	1	8	yes	—
327	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	16	yes	—
329	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
330	C₂×C₄	C₂×C₄×Dic₄₇	1	8	yes	—
331	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
332	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
333	C₂×C₄	#13093982	1	4	yes	—
334	C₂×C₄	#13093986	1	4	yes	—
335	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
336	C₂×C₄	#13093989	1	4	yes	—
337	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
338	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
339	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
340	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
341	C₂²	C₂²×C₄×Dic₄₇	1	2	yes	—
342	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
343	C₂²	#117×D₄₇	1	2	yes	—
344	C₂²	C₂×#13093982	1	1	yes	characteristic
345	C₂²	C₄×D₄×D₄₇	1	4	yes	—
346	C₂²	C₂×#13093986	1	1	yes	characteristic
347	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
348	C₂²	C₄×Q₈×D₄₇	1	4	yes	—
349	C₂²	C₂×#13093989	1	1	yes	characteristic
350	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
351	C₂²	C₄×#10625352	1	4	yes	—
352	C₂²	#15689591	1	2	yes	—
353	C₂²	C₄×#10625354	1	4	yes	—
354	C₂²	#41×Dic₄₇	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	2	16	no	—
357	C₄	—	47	16	no	—
358	C₄	—	94	8	no	—
359	C₄	—	94	16	no	—
360	C₄	C₄²×Dic₄₇	1	8	yes	complemented
361	C₄	C₄⋊C₄×Dic₄₇	1	8	yes	direct product factor
362	C₂	C₂×C₄²×Dic₄₇	1	1	yes	characteristic
363	C₂	C₄×C₄⋊C₄×D₄₇	1	2	yes	—
364	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
365	C₂	C₄×#13093982	1	2	yes	—
366	C₂	#117×Dic₄₇	1	1	yes	characteristic
367	C₂	C₄×#13093986	1	2	yes	—
368	C₂	C₄×D₄×Dic₄₇	1	2	yes	—
369	C₂	C₄×#13093989	1	2	yes	—
370	C₂	C₄×Q₈×Dic₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical, cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₄²×C₄⋊C₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
15. C₄⋊C₄×Dic₄₇	C₄	direct (N × H)
16. C₄×C₄⋊Dic₄₇	C₄	semidirect
20. C₄²×Dic₄₇	C₄	semidirect
24. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
98. C₄⋊C₄×C₄₇	C₄²	semidirect
100. C₄²×C₄₇	C₄²	semidirect
101. C₄⋊Dic₄₇	C₄²	semidirect
106. C₄×Dic₄₇	C₄²	semidirect
107. C₄×Dic₄₇	C₄⋊C₄	direct (N × H)
172. C₄×C₄₇	C₄³	semidirect
173. C₄×C₄₇	C₄×C₄⋊C₄	semidirect
176. Dic₄₇	C₄×C₄⋊C₄	direct (N × H)
205. C₄×C₄⋊C₄	Dic₄₇	direct (N × H)
211. C₄₇	C₄²×C₄⋊C₄	semidirect
285. C₄⋊C₄	C₄×Dic₄₇	direct (N × H)
293. C₄²	C₄×Dic₄₇	semidirect
360. C₄	C₄²×Dic₄₇	semidirect
361. C₄	C₄⋊C₄×Dic₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄²×Dic₄₇	2
C₄×C₄₇⋊#95	2
#95×Dic₄₇	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄²×C₄⋊C₄	47

Subgroups — C4×C4⋊C4×Dic47 #26137356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊C₄×Dic₄₇ #26137356