Subgroups — C₂×C₄²×C₂²⋊D₄₇ #26374469

Order 12032.

5694 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₂²⋊D₄₇	C₂	1	3	yes	maximal
2	C₂²×C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₂²⋊D₄₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄×Dic₄₇⋊C₄	C₂	1	3	yes	maximal, complemented
5	C₂×C₄×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	3	yes	maximal, complemented
7	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
10	C₂³×C₄×D₄₇	C₂²	1	3	yes	—
11	C₂×C₄×C₂²⋊D₄₇	C₄	1	48	yes	direct product factor
12	C₂×C₄×C₂²⋊D₄₇	C₂²	1	24	yes	—
13	C₂²×Dic₄₇⋊C₄	C₂²	1	3	yes	—
14	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
15	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
16	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
17	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
18	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
19	C₂×C₄²×D₄₇	—	2	8	no	—
20	C₂×C₄²×D₄₇	C₂²	1	8	yes	complemented
21	C₄×Dic₄₇⋊C₄	C₂²	1	24	yes	complemented
22	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	24	yes	complemented
23	C₄×C₂²⋊Dic₄₇	C₂²	1	24	yes	complemented
24	C₂×C₄₇⋊#95	C₂²	1	6	yes	—
25	C₄²×Dic₄₇	C₂²	1	8	yes	complemented
26	C₂⁴×C₄×C₄₇	C₂²	1	3	yes	—
27	C₂²×C₄²×C₄₇	—	2	8	no	—
28	C₂²×C₄²×C₄₇	C₂²	1	3	yes	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	8	yes	complemented
31	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
32	C₂²×C₂²⋊D₄₇	C₂×C₄	1	24	yes	—
33	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
34	C₂³×Dic₄₇	C₂³	1	3	yes	—
35	C₂³×Dic₄₇	C₂³	1	3	yes	—
36	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
37	C₂²×C₄×D₄₇	—	2	12	no	—
38	C₂²×C₄×D₄₇	—	2	12	no	—
39	C₂²×C₄×D₄₇	C₂×C₄	1	24	yes	complemented
40	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
41	C₄×C₂²⋊D₄₇	C₂×C₄	1	192	yes	direct product factor
42	C₂×Dic₄₇⋊C₄	C₂×C₄	1	24	yes	complemented
43	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	—
44	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	24	yes	complemented
45	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
46	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	24	yes	complemented
47	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
48	C₂×C₄×Dic₄₇	—	2	12	no	—
49	C₂×C₄×Dic₄₇	—	2	12	no	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	complemented
51	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
53	C₂×C₄×Dic₄₇	C₂³	1	12	yes	—
54	C₄²×D₄₇	—	2	32	no	—
55	C₄₇⋊#95	C₂³	1	24	yes	—
56	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	—	2	12	no	—
58	C₂³×C₄×C₄₇	—	2	12	no	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	24	yes	complemented
60	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
63	C₂×C₄²×C₄₇	—	2	12	no	—
64	C₂×C₄²×C₄₇	—	2	32	no	—
65	C₂×C₄²×C₄₇	D₄	1	8	yes	complemented
66	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
68	C₂⁴×C₄₇	—	2	2	no	—
69	C₂⁴×C₄₇	—	2	6	no	—
70	C₂⁴×C₄₇	C₂²×C₄	1	12	yes	—
71	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
72	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
73	C₂³×D₄₇	—	2	2	no	—
74	C₂³×D₄₇	—	2	6	no	—
75	C₂³×D₄₇	C₂²×C₄	1	12	yes	—
76	C₂³×D₄₇	C₂⁴	1	2	yes	—
77	C₂²×C₄×C₄₇	—	2	6	no	—
78	C₂²×C₄×C₄₇	—	2	6	no	—
79	C₂²×C₄×C₄₇	—	2	96	no	—
80	C₂²×C₄×C₄₇	—	2	24	no	—
81	C₂²×C₄×C₄₇	—	2	24	no	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	48	yes	complemented
85	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
86	C₂²×C₄×C₄₇	#41	1	12	yes	—
87	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
88	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
89	C₂×C₂²⋊D₄₇	C₄²	1	64	yes	direct product factor
90	C₂×C₂²⋊D₄₇	C₂²×C₄	1	48	yes	—
91	C₂²×Dic₄₇	—	2	6	no	—
92	C₂²×Dic₄₇	—	2	12	no	—
93	C₂²×Dic₄₇	—	2	6	no	—
94	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
97	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
98	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
99	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
100	C₂×C₄×D₄₇	—	2	96	no	—
101	C₂×C₄×D₄₇	—	2	24	no	—
102	C₂×C₄×D₄₇	—	2	24	no	—
103	C₂×C₄×D₄₇	C₂²×C₄	1	48	yes	complemented
104	C₄²×C₄₇	—	2	24	no	—
105	C₄²×C₄₇	C₂×D₄	1	16	yes	complemented
106	C₂²⋊Dic₄₇	C₂²×C₄	1	48	yes	complemented
107	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	48	yes	complemented
108	Dic₄₇⋊C₄	C₂²×C₄	1	48	yes	complemented
109	C₄×Dic₄₇	—	2	24	no	—
110	C₄×Dic₄₇	—	2	24	no	—
111	C₄×Dic₄₇	C₂²×C₄	1	48	yes	complemented
112	C₂³×C₄₇	—	2	24	no	—
113	C₂³×C₄₇	—	2	24	no	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	—	2	6	no	—
116	C₂³×C₄₇	C₂×C₄²	1	16	yes	complemented
117	C₂³×C₄₇	C₂³×C₄	1	12	yes	—
118	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
119	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
120	C₂³×C₄₇	C₂×#41	1	6	yes	—
121	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
122	C₂²×D₄₇	—	2	24	no	—
123	C₂²×D₄₇	—	2	24	no	—
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	2	6	no	—
126	C₂²×D₄₇	C₂×C₄²	1	16	yes	complemented
127	C₂²×D₄₇	C₂³×C₄	1	12	yes	—
128	C₂×C₄×C₄₇	—	2	24	no	—
129	C₂×C₄×C₄₇	—	2	6	no	—
130	C₂×C₄×C₄₇	—	2	6	no	—
131	C₂×C₄×C₄₇	—	2	96	no	—
132	C₂×C₄×C₄₇	C₄×D₄	1	48	yes	complemented
133	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
134	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	—
135	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
136	C₂×C₄×C₄₇	C₂×#41	1	12	yes	—
137	C₂²⋊D₄₇	C₂×C₄²	1	64	yes	direct product factor
138	C₂×Dic₄₇	—	2	24	no	—
139	C₂×Dic₄₇	—	2	24	no	—
140	C₂×Dic₄₇	—	2	6	no	—
141	C₂×Dic₄₇	—	2	12	no	—
142	C₂×Dic₄₇	—	2	6	no	—
143	C₂×Dic₄₇	C₂×C₄²	1	16	yes	complemented
144	C₂×Dic₄₇	C₂³×C₄	1	12	yes	—
145	C₂×Dic₄₇	C₂³×C₄	1	12	yes	—
146	C₂×Dic₄₇	C₂³×C₄	1	12	yes	—
147	C₄×D₄₇	—	2	96	no	—
148	C₂×C₄²×D₄	—	47	1	no	maximal, Sylow
149	C₂²×C₄₇	—	2	12	no	—
150	C₂²×C₄₇	—	2	12	no	—
151	C₂²×C₄₇	—	2	32	no	—
152	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
153	C₂²×C₄₇	C₂²×C₄²	1	8	yes	complemented
154	C₂²×C₄₇	C₂×C₄×D₄	1	12	yes	—
155	C₂²×C₄₇	C₄×#41	1	12	yes	—
156	C₂²×C₄₇	C₂⁴×C₄	1	3	yes	—
157	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
158	C₂²×C₄₇	C₂²×#41	1	3	yes	—
159	C₂×D₄₇	—	2	12	no	—
160	C₂×D₄₇	—	2	12	no	—
161	C₂×D₄₇	—	2	32	no	—
162	C₂×D₄₇	C₂²×C₄²	1	8	yes	complemented
163	C₄×C₄₇	—	2	12	no	—
164	C₄×C₄₇	C₂×C₄×D₄	1	24	yes	complemented
165	Dic₄₇	—	2	12	no	—
166	Dic₄₇	—	2	12	no	—
167	Dic₄₇	C₂²×C₄²	1	8	yes	complemented
168	C₂²×C₄×D₄	—	47	3	no	—
169	C₂³×C₄²	—	47	1	no	—
170	C₂³×C₄²	D₄₇	1	1	yes	characteristic, complemented
171	C₄²×D₄	—	47	16	no	—
172	C₂×C₄×C₄⋊C₄	—	47	3	no	—
173	C₂×C₄×C₂²⋊C₄	—	47	3	no	—
174	C₂×C₄×C₂²⋊C₄	—	47	3	no	—
175	C₂×C₄³	—	47	1	no	—
176	C₂×C₄₇	—	2	8	no	—
177	C₂×C₄₇	C₄²×D₄	1	8	yes	complemented
178	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
179	C₂×C₄₇	C₂²×C₄×D₄	1	3	yes	—
180	C₂×C₄₇	C₂×C₄×#41	1	3	yes	—
181	D₄₇	—	2	8	no	—
182	C₂³×D₄	—	47	1	no	—
183	C₂⁴×C₄	—	47	3	no	—
184	C₂⁴×C₄	C₂×D₄₇	1	3	yes	—
185	C₂×C₄×D₄	—	47	48	no	—
186	C₂×C₄×D₄	—	47	24	no	—
187	C₂²×C₄⋊C₄	—	47	3	no	—
188	C₂²×C₂²⋊C₄	—	47	3	no	—
189	C₂²×C₂²⋊C₄	—	47	3	no	—
190	C₂²×C₄²	—	2	8	no	—
191	C₂²×C₄²	—	47	3	no	—
192	C₂²×C₄²	—	47	3	no	—
193	C₂²×C₄²	—	47	3	no	—
194	C₂²×C₄²	—	47	8	no	—
195	C₂²×C₄²	—	94	8	no	—
196	C₂²×C₄²	C₂×D₄₇	1	3	yes	—
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	C₂²×C₄²	C₂×D₄₇	1	8	yes	complemented
199	C₄×C₄⋊C₄	—	47	24	no	—
200	C₄×C₂²⋊C₄	—	47	24	no	—
201	C₄×C₂²⋊C₄	—	47	24	no	—
202	C₂×#95	—	47	6	no	—
203	C₄³	—	47	8	no	—
204	C₄₇	C₂×C₄²×D₄	1	1	yes	characteristic, complemented, Sylow
205	C₂⁵	—	47	1	no	—
206	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
207	C₂²×D₄	—	47	24	no	—
208	C₂²×D₄	—	47	4	no	—
209	C₂³×C₄	—	2	12	no	—
210	C₂³×C₄	—	2	12	no	—
211	C₂³×C₄	—	47	1	no	—
212	C₂³×C₄	—	47	3	no	—
213	C₂³×C₄	—	47	3	no	—
214	C₂³×C₄	—	47	24	no	—
215	C₂³×C₄	—	47	12	no	—
216	C₂³×C₄	—	94	12	no	—
217	C₂³×C₄	—	94	12	no	—
218	C₂³×C₄	C₄×D₄₇	1	24	yes	complemented
219	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
220	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
221	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
222	C₄×D₄	—	47	192	no	—
223	C₂×C₄⋊C₄	—	47	24	no	—
224	C₂×C₄⋊C₄	—	47	12	no	—
225	C₂×C₂²⋊C₄	—	47	24	no	—
226	C₂×C₂²⋊C₄	—	47	12	no	—
227	C₂×C₂²⋊C₄	—	47	24	no	—
228	C₂×C₂²⋊C₄	—	47	12	no	—
229	C₂×C₄²	—	2	12	no	—
230	C₂×C₄²	—	2	32	no	—
231	C₂×C₄²	—	47	24	no	—
232	C₂×C₄²	—	47	12	no	—
233	C₂×C₄²	—	47	12	no	—
234	C₂×C₄²	—	47	12	no	—
235	C₂×C₄²	—	94	12	no	—
236	C₂×C₄²	—	94	12	no	—
237	C₂×C₄²	—	94	32	no	—
238	C₂×C₄²	C₂²⋊D₄₇	1	8	yes	direct product factor
239	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
240	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
241	#95	—	47	24	no	—
242	C₂⁴	—	2	2	no	—
243	C₂⁴	—	2	6	no	—
244	C₂⁴	—	47	12	no	—
245	C₂⁴	—	47	2	no	—
246	C₂⁴	—	94	2	no	—
247	C₂⁴	—	94	6	no	—
248	C₂⁴	C₂×C₄×D₄₇	1	12	yes	—
249	C₂⁴	C₂³×D₄₇	1	2	yes	—
250	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
251	C₂×D₄	—	47	64	no	—
252	C₂×D₄	—	47	48	no	—
253	C₂²×C₄	—	2	6	no	—
254	C₂²×C₄	—	2	6	no	—
255	C₂²×C₄	—	2	96	no	—
256	C₂²×C₄	—	2	24	no	—
257	C₂²×C₄	—	2	24	no	—
258	C₂²×C₄	—	47	12	no	—
259	C₂²×C₄	—	47	2	no	—
260	C₂²×C₄	—	47	12	no	—
261	C₂²×C₄	—	47	12	no	—
262	C₂²×C₄	—	47	6	no	—
263	C₂²×C₄	—	47	6	no	—
264	C₂²×C₄	—	47	48	no	—
265	C₂²×C₄	—	94	6	no	—
266	C₂²×C₄	—	94	12	no	—
267	C₂²×C₄	—	94	6	no	—
268	C₂²×C₄	—	94	96	no	—
269	C₂²×C₄	—	94	24	no	—
270	C₂²×C₄	—	94	24	no	—
271	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
272	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
273	C₂²×C₄	C₂×C₄×D₄₇	1	48	yes	complemented
274	C₂²×C₄	#10625350	1	12	yes	—
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
276	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
277	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
278	C₄⋊C₄	—	47	48	no	—
279	C₂²⋊C₄	—	47	48	no	—
280	C₂²⋊C₄	—	47	48	no	—
281	C₄²	—	2	24	no	—
282	C₄²	—	47	48	no	—
283	C₄²	—	94	24	no	—
284	C₄²	—	94	24	no	—
285	C₄²	C₂×C₂²⋊D₄₇	1	16	yes	direct product factor
286	C₂³	—	2	24	no	—
287	C₂³	—	2	24	no	—
288	C₂³	—	2	2	no	—
289	C₂³	—	2	6	no	—
290	C₂³	—	47	16	no	—
291	C₂³	—	47	12	no	—
292	C₂³	—	94	24	no	—
293	C₂³	—	94	24	no	—
294	C₂³	—	94	2	no	—
295	C₂³	—	94	6	no	—
296	C₂³	C₄²×D₄₇	1	16	yes	complemented
297	C₂³	C₂²×C₄×D₄₇	1	12	yes	—
298	C₂³	C₂²×C₄×D₄₇	1	6	yes	—
299	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
300	C₂³	C₂×#10625350	1	6	yes	—
301	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
302	D₄	—	47	64	no	—
303	C₂×C₄	—	2	24	no	—
304	C₂×C₄	—	2	6	no	—
305	C₂×C₄	—	2	6	no	—
306	C₂×C₄	—	2	96	no	—
307	C₂×C₄	—	47	16	no	—
308	C₂×C₄	—	47	12	no	—
309	C₂×C₄	—	47	12	no	—
310	C₂×C₄	—	47	12	no	—
311	C₂×C₄	—	94	24	no	—
312	C₂×C₄	—	94	24	no	—
313	C₂×C₄	—	94	6	no	—
314	C₂×C₄	—	94	12	no	—
315	C₂×C₄	—	94	6	no	—
316	C₂×C₄	—	94	96	no	—
317	C₂×C₄	C₄×C₂²⋊D₄₇	1	48	yes	direct product factor
318	C₂×C₄	C₂²×C₄×D₄₇	1	12	yes	—
319	C₂×C₄	C₂²×C₄×D₄₇	1	12	yes	—
320	C₂×C₄	C₂²×C₂²⋊D₄₇	1	12	yes	—
321	C₂×C₄	C₂×#10625350	1	12	yes	—
322	C₂²	—	2	12	no	—
323	C₂²	—	2	12	no	—
324	C₂²	—	2	32	no	—
325	C₂²	—	47	8	no	—
326	C₂²	—	94	12	no	—
327	C₂²	—	94	12	no	—
328	C₂²	—	94	32	no	—
329	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
330	C₂²	C₂×C₄²×D₄₇	1	8	yes	complemented
331	C₂²	C₂×C₄×C₂²⋊D₄₇	1	12	yes	—
332	C₂²	C₄×#10625350	1	12	yes	—
333	C₂²	C₂³×C₄×D₄₇	1	3	yes	—
334	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂²	C₂²×#10625350	1	3	yes	—
336	C₄	—	2	12	no	—
337	C₄	—	47	8	no	—
338	C₄	—	94	12	no	—
339	C₄	—	94	12	no	—
340	C₄	C₂×C₄×C₂²⋊D₄₇	1	24	yes	direct product factor
341	C₂	—	2	8	no	—
342	C₂	—	94	8	no	—
343	C₂	C₄²×C₂²⋊D₄₇	1	8	yes	direct product factor
344	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
345	C₂	C₂²×C₄×C₂²⋊D₄₇	1	3	yes	—
346	C₂	C₂×C₄×#10625350	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×C₂²⋊D₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×C₄²×D₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄² ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄²×D₄₇	C₂	semidirect
3. C₄²×C₂²⋊D₄₇	C₂	direct (N × H)
4. C₂×C₄×Dic₄₇⋊C₄	C₂	semidirect
5. C₂×C₄×(C₂×D₄₇)⋊C₄	C₂	semidirect
6. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
7. C₂×C₄²×Dic₄₇	C₂	semidirect
8. C₂³×C₄²×C₄₇	C₂	semidirect
11. C₂×C₄×C₂²⋊D₄₇	C₄	direct (N × H)
20. C₂×C₄²×D₄₇	C₂²	semidirect
21. C₄×Dic₄₇⋊C₄	C₂²	semidirect
22. C₄×(C₂×D₄₇)⋊C₄	C₂²	semidirect
23. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
25. C₄²×Dic₄₇	C₂²	semidirect
30. C₂²×C₄²×C₄₇	C₂²	semidirect
39. C₂²×C₄×D₄₇	C₂×C₄	semidirect
41. C₄×C₂²⋊D₄₇	C₂×C₄	direct (N × H)
42. C₂×Dic₄₇⋊C₄	C₂×C₄	semidirect
44. C₂×C₂²⋊Dic₄₇	C₂×C₄	semidirect
46. C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
50. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
59. C₂³×C₄×C₄₇	C₂×C₄	semidirect
65. C₂×C₄²×C₄₇	D₄	semidirect
84. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₄₇	C₄²	direct (N × H)
103. C₂×C₄×D₄₇	C₂²×C₄	semidirect
105. C₄²×C₄₇	C₂×D₄	semidirect
106. C₂²⋊Dic₄₇	C₂²×C₄	semidirect
107. (C₂×D₄₇)⋊C₄	C₂²×C₄	semidirect
108. Dic₄₇⋊C₄	C₂²×C₄	semidirect
111. C₄×Dic₄₇	C₂²×C₄	semidirect
116. C₂³×C₄₇	C₂×C₄²	semidirect
126. C₂²×D₄₇	C₂×C₄²	semidirect
132. C₂×C₄×C₄₇	C₄×D₄	semidirect
137. C₂²⋊D₄₇	C₂×C₄²	direct (N × H)
143. C₂×Dic₄₇	C₂×C₄²	semidirect
153. C₂²×C₄₇	C₂²×C₄²	semidirect
162. C₂×D₄₇	C₂²×C₄²	semidirect
164. C₄×C₄₇	C₂×C₄×D₄	semidirect
167. Dic₄₇	C₂²×C₄²	semidirect
170. C₂³×C₄²	D₄₇	semidirect
177. C₂×C₄₇	C₄²×D₄	semidirect
198. C₂²×C₄²	C₂×D₄₇	semidirect
204. C₄₇	C₂×C₄²×D₄	semidirect
218. C₂³×C₄	C₄×D₄₇	semidirect
238. C₂×C₄²	C₂²⋊D₄₇	direct (N × H)
273. C₂²×C₄	C₂×C₄×D₄₇	semidirect
285. C₄²	C₂×C₂²⋊D₄₇	direct (N × H)
296. C₂³	C₄²×D₄₇	semidirect
317. C₂×C₄	C₄×C₂²⋊D₄₇	direct (N × H)
330. C₂²	C₂×C₄²×D₄₇	semidirect
340. C₄	C₂×C₄×C₂²⋊D₄₇	direct (N × H)
343. C₂	C₄²×C₂²⋊D₄₇	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×C₄×C₂²⋊D₄₇	2
C₂²×C₄²×D₄₇	2
C₄²×C₂²⋊D₄₇	2
C₂×C₄×Dic₄₇⋊C₄	2
C₂×C₄×(C₂×D₄₇)⋊C₄	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂×C₄²×Dic₄₇	2
C₂³×C₄²×C₄₇	2
C₂×C₄²×D₄	47

Subgroups — C2×C42×C22⋊D47 #26374469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄²×C₂²⋊D₄₇ #26374469