Subgroups — C₂²×C₄×(C₂×D₄₇)⋊C₄ #26374452

Order 12032.

9534 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×(C₂×D₄₇)⋊C₄	C₂	1	2	yes	maximal
3	C₂³×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×(C₂×D₄₇)⋊C₄	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₄₇	C₂²	1	1	yes	characteristic
8	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
10	C₂³×C₄×D₄₇	—	2	8	no	—
11	C₂³×C₄×D₄₇	—	2	8	no	—
12	C₂³×C₄×D₄₇	C₄	1	16	yes	complemented
13	C₂³×C₄×D₄₇	C₂²	1	12	yes	—
14	C₂²×(C₂×D₄₇)⋊C₄	C₄	1	32	yes	direct product factor
15	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	24	yes	—
16	C₂²×C₄×Dic₄₇	—	2	8	no	—
17	C₂²×C₄×Dic₄₇	C₂²	1	12	yes	complemented
18	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	64	yes	direct product factor
19	C₂×C₄₇⋊#95	C₂²	1	24	yes	complemented
20	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	—	2	8	no	—
23	C₂²×C₄²×C₄₇	C₂²	1	12	yes	complemented
24	C₂⁴×D₄₇	—	2	4	no	—
25	C₂⁴×D₄₇	—	2	4	no	—
26	C₂⁴×D₄₇	—	2	8	no	—
27	C₂⁴×D₄₇	C₂×C₄	1	16	yes	—
28	C₂⁴×D₄₇	C₂×C₄	1	8	yes	—
29	C₂⁴×D₄₇	C₂³	1	6	yes	—
30	C₂³×Dic₄₇	—	2	8	no	—
31	C₂³×Dic₄₇	—	2	4	no	—
32	C₂³×Dic₄₇	—	2	4	no	—
33	C₂³×Dic₄₇	—	2	8	no	—
34	C₂³×Dic₄₇	C₂×C₄	1	8	yes	—
35	C₂³×Dic₄₇	C₂×C₄	1	16	yes	complemented
36	C₂³×Dic₄₇	C₂³	1	6	yes	—
37	C₂³×Dic₄₇	C₂³	1	12	yes	—
38	C₂²×C₄×D₄₇	—	2	128	no	—
39	C₂²×C₄×D₄₇	—	2	48	no	—
40	C₂²×C₄×D₄₇	—	2	48	no	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	96	yes	complemented
42	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
43	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	192	yes	direct product factor
44	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
45	C₂×C₄×Dic₄₇	—	2	48	no	—
46	C₂×C₄×Dic₄₇	C₂³	1	16	yes	complemented
47	C₄₇⋊#95	C₂³	1	32	yes	complemented
48	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	—	2	8	no	—
50	C₂³×C₄×C₄₇	—	2	8	no	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
53	C₂³×C₄×C₄₇	D₄	1	8	yes	—
54	C₂³×C₄×C₄₇	D₄	1	8	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
57	C₂×C₄²×C₄₇	—	2	48	no	—
58	C₂×C₄²×C₄₇	C₂³	1	16	yes	complemented
59	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
60	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
61	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
62	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
63	C₂⁴×C₄₇	#41	1	8	yes	—
64	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
65	C₂³×D₄₇	—	2	32	no	—
66	C₂³×D₄₇	—	2	32	no	—
67	C₂³×D₄₇	—	2	64	no	—
68	C₂³×D₄₇	—	2	64	no	—
69	C₂³×D₄₇	—	2	12	no	—
70	C₂³×D₄₇	—	2	12	no	—
71	C₂³×D₄₇	—	2	24	no	—
72	C₂³×D₄₇	C₄²	1	64	yes	complemented
73	C₂³×D₄₇	C₂²×C₄	1	48	yes	—
74	C₂³×D₄₇	C₂²×C₄	1	24	yes	—
75	C₂³×D₄₇	C₂⁴	1	4	yes	—
76	C₂²×C₄×C₄₇	—	2	64	no	—
77	C₂²×C₄×C₄₇	—	2	24	no	—
78	C₂²×C₄×C₄₇	—	2	24	no	—
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	64	yes	complemented
80	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	48	yes	complemented
82	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	—
83	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	—
84	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
86	C₂²×Dic₄₇	—	2	32	no	—
87	C₂²×Dic₄₇	—	2	64	no	—
88	C₂²×Dic₄₇	—	2	24	no	—
89	C₂²×Dic₄₇	—	2	12	no	—
90	C₂²×Dic₄₇	—	2	12	no	—
91	C₂²×Dic₄₇	—	2	24	no	—
92	C₂²×Dic₄₇	C₂²×C₄	1	24	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	48	yes	complemented
94	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
95	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
96	C₂×C₄×D₄₇	—	2	384	no	—
97	C₂×C₄×D₄₇	—	2	32	no	—
98	C₂×C₄×D₄₇	—	2	32	no	—
99	C₂×C₄×D₄₇	C₂²×C₄	1	64	yes	complemented
100	C₄²×C₄₇	—	2	32	no	—
101	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	128	yes	direct product factor
102	C₄×Dic₄₇	—	2	32	no	—
103	C₂³×C₄₇	C₂×C₄²	1	16	yes	—
104	C₂³×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
105	C₂³×C₄₇	#117	1	16	yes	—
106	C₂³×C₄₇	C₄×D₄	1	32	yes	—
107	C₂³×C₄₇	C₄×D₄	1	32	yes	—
108	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
109	C₂³×C₄₇	C₂³×C₄	1	12	yes	—
110	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
111	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
112	C₂³×C₄₇	C₂×#41	1	12	yes	—
113	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
114	C₂²×D₄₇	—	2	48	no	—
115	C₂²×D₄₇	—	2	48	no	—
116	C₂²×D₄₇	—	2	96	no	—
117	C₂²×D₄₇	—	2	96	no	—
118	C₂²×D₄₇	—	2	4	no	—
119	C₂²×D₄₇	—	2	4	no	—
120	C₂²×D₄₇	—	2	8	no	—
121	C₂²×D₄₇	—	2	256	no	—
122	C₂²×D₄₇	C₂×C₄²	1	96	yes	complemented
123	C₂²×D₄₇	C₂³×C₄	1	16	yes	—
124	C₂²×D₄₇	C₂³×C₄	1	8	yes	—
125	C₂×C₄×C₄₇	—	2	96	no	—
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	96	yes	complemented
129	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
130	C₂×C₄×C₄₇	C₂³×C₄	1	16	yes	complemented
131	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
132	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
133	C₂×Dic₄₇	—	2	48	no	—
134	C₂×Dic₄₇	—	2	96	no	—
135	C₂×Dic₄₇	—	2	8	no	—
136	C₂×Dic₄₇	—	2	4	no	—
137	C₂×Dic₄₇	—	2	4	no	—
138	C₂×Dic₄₇	—	2	8	no	—
139	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
140	C₂×Dic₄₇	C₂³×C₄	1	16	yes	complemented
141	C₄×D₄₇	—	2	128	no	—
142	C₂²×C₄×C₂²⋊C₄	—	47	1	no	maximal, Sylow
143	C₂²×C₄₇	C₄×C₂²⋊C₄	1	64	yes	complemented
144	C₂²×C₄₇	C₂²×C₄²	1	12	yes	—
145	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	12	yes	—
146	C₂²×C₄₇	C₂×#117	1	12	yes	—
147	C₂²×C₄₇	C₂×C₄×D₄	1	24	yes	—
148	C₂²×C₄₇	C₂×C₄×D₄	1	24	yes	—
149	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
150	C₂²×C₄₇	C₂⁴×C₄	1	2	yes	—
151	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
152	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
153	C₂²×C₄₇	C₂²×#41	1	2	yes	—
154	C₂×D₄₇	—	2	8	no	—
155	C₂×D₄₇	—	2	8	no	—
156	C₂×D₄₇	—	2	16	no	—
157	C₂×D₄₇	—	2	16	no	—
158	C₂×D₄₇	—	2	192	no	—
159	C₂×D₄₇	C₂²×C₄²	1	16	yes	complemented
160	C₄×C₄₇	—	2	16	no	—
161	C₄×C₄₇	C₂²×C₂²⋊C₄	1	16	yes	complemented
162	Dic₄₇	—	2	8	no	—
163	Dic₄₇	—	2	16	no	—
164	C₂⁵×C₄	—	47	1	no	—
165	C₂³×C₂²⋊C₄	—	47	2	no	—
166	C₂³×C₄²	—	47	1	no	—
167	C₂³×C₄²	D₄₇	1	1	yes	characteristic, complemented
168	C₂×C₄×C₂²⋊C₄	—	47	24	no	—
169	C₂²×#95	—	47	2	no	—
170	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	24	yes	complemented
171	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
172	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
174	C₂×C₄₇	C₂²×C₄×D₄	1	2	yes	—
175	C₂×C₄₇	C₂²×C₄×D₄	1	2	yes	—
176	D₄₇	—	2	16	no	—
177	C₂⁶	—	47	1	no	—
178	C₂⁴×C₄	—	47	1	no	—
179	C₂⁴×C₄	—	47	2	no	—
180	C₂⁴×C₄	—	47	16	no	—
181	C₂⁴×C₄	—	47	12	no	—
182	C₂⁴×C₄	—	94	8	no	—
183	C₂⁴×C₄	—	94	8	no	—
184	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
185	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	—	47	32	no	—
187	C₂²×C₂²⋊C₄	—	47	24	no	—
188	C₂²×C₄²	—	2	8	no	—
189	C₂²×C₄²	—	47	12	no	—
190	C₂²×C₄²	—	94	8	no	—
191	C₂²×C₄²	C₂×D₄₇	1	12	yes	complemented
192	C₄×C₂²⋊C₄	—	47	64	no	—
193	C₂×#95	—	47	24	no	—
194	C₄₇	C₂²×C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
195	C₂⁵	—	47	16	no	—
196	C₂⁵	—	47	8	no	—
197	C₂⁵	—	47	6	no	—
198	C₂⁵	—	94	4	no	—
199	C₂⁵	—	94	8	no	—
200	C₂⁵	—	94	4	no	—
201	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
202	C₂³×C₄	—	2	8	no	—
203	C₂³×C₄	—	2	8	no	—
204	C₂³×C₄	—	47	16	no	—
205	C₂³×C₄	—	47	8	no	—
206	C₂³×C₄	—	47	12	no	—
207	C₂³×C₄	—	47	6	no	—
208	C₂³×C₄	—	47	96	no	—
209	C₂³×C₄	—	47	16	no	—
210	C₂³×C₄	—	94	4	no	—
211	C₂³×C₄	—	94	8	no	—
212	C₂³×C₄	—	94	8	no	—
213	C₂³×C₄	—	94	4	no	—
214	C₂³×C₄	—	94	128	no	—
215	C₂³×C₄	—	94	48	no	—
216	C₂³×C₄	—	94	48	no	—
217	C₂³×C₄	C₄×D₄₇	1	8	yes	—
218	C₂³×C₄	C₄×D₄₇	1	16	yes	complemented
219	C₂³×C₄	D₁₈₈	1	8	yes	—
220	C₂³×C₄	C₂²⋊D₄₇	1	8	yes	—
221	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
222	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
223	C₂×C₂²⋊C₄	—	47	192	no	—
224	C₂×C₂²⋊C₄	—	47	32	no	—
225	C₂×C₄²	—	2	48	no	—
226	C₂×C₄²	—	47	16	no	—
227	C₂×C₄²	—	94	48	no	—
228	C₂×C₄²	C₂²×D₄₇	1	16	yes	complemented
229	#95	—	47	32	no	—
230	C₂⁴	—	47	64	no	—
231	C₂⁴	—	47	48	no	—
232	C₂⁴	—	47	24	no	—
233	C₂⁴	—	47	4	no	—
234	C₂⁴	—	94	32	no	—
235	C₂⁴	—	94	32	no	—
236	C₂⁴	—	94	64	no	—
237	C₂⁴	—	94	64	no	—
238	C₂⁴	—	94	12	no	—
239	C₂⁴	—	94	12	no	—
240	C₂⁴	—	94	24	no	—
241	C₂⁴	C₂×C₄×D₄₇	1	4	yes	—
242	C₂⁴	C₂×C₄×D₄₇	1	8	yes	—
243	C₂⁴	C₂×D₁₈₈	1	4	yes	—
244	C₂⁴	#10625350	1	8	yes	—
245	C₂⁴	C₂×C₂²⋊D₄₇	1	4	yes	—
246	C₂⁴	C₂³×D₄₇	1	3	yes	—
247	C₂²×C₄	—	2	64	no	—
248	C₂²×C₄	—	2	24	no	—
249	C₂²×C₄	—	2	24	no	—
250	C₂²×C₄	—	47	24	no	—
251	C₂²×C₄	—	47	48	no	—
252	C₂²×C₄	—	47	4	no	—
253	C₂²×C₄	—	47	8	no	—
254	C₂²×C₄	—	47	64	no	—
255	C₂²×C₄	—	94	32	no	—
256	C₂²×C₄	—	94	64	no	—
257	C₂²×C₄	—	94	12	no	—
258	C₂²×C₄	—	94	24	no	—
259	C₂²×C₄	—	94	12	no	—
260	C₂²×C₄	—	94	24	no	—
261	C₂²×C₄	—	94	384	no	—
262	C₂²×C₄	—	94	32	no	—
263	C₂²×C₄	—	94	32	no	—
264	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	64	yes	direct product factor
265	C₂²×C₄	C₂×C₄×D₄₇	1	24	yes	—
266	C₂²×C₄	C₂×C₄×D₄₇	1	48	yes	complemented
267	C₂²×C₄	C₂×D₁₈₈	1	24	yes	—
268	C₂²×C₄	C₂×C₂²⋊D₄₇	1	24	yes	—
269	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
270	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
271	C₂²⋊C₄	—	47	128	no	—
272	C₄²	—	2	32	no	—
273	C₄²	—	94	32	no	—
274	C₂³	—	47	96	no	—
275	C₂³	—	47	16	no	—
276	C₂³	—	47	8	no	—
277	C₂³	—	94	256	no	—
278	C₂³	—	94	48	no	—
279	C₂³	—	94	48	no	—
280	C₂³	—	94	96	no	—
281	C₂³	—	94	96	no	—
282	C₂³	—	94	4	no	—
283	C₂³	—	94	4	no	—
284	C₂³	—	94	8	no	—
285	C₂³	C₄²×D₄₇	1	16	yes	—
286	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	16	yes	—
287	C₂³	#13093981	1	16	yes	—
288	C₂³	C₄×C₂²⋊D₄₇	1	32	yes	—
289	C₂³	C₄×D₁₈₈	1	32	yes	—
290	C₂³	C₂²×C₄×D₄₇	1	6	yes	—
291	C₂³	C₂²×C₄×D₄₇	1	12	yes	—
292	C₂³	C₂²×C₂²⋊D₄₇	1	6	yes	—
293	C₂³	C₂²×D₁₈₈	1	6	yes	—
294	C₂³	C₂×#10625350	1	12	yes	—
295	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
296	C₂×C₄	—	2	96	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	47	8	no	—
300	C₂×C₄	—	47	16	no	—
301	C₂×C₄	—	94	48	no	—
302	C₂×C₄	—	94	96	no	—
303	C₂×C₄	—	94	4	no	—
304	C₂×C₄	—	94	8	no	—
305	C₂×C₄	—	94	4	no	—
306	C₂×C₄	—	94	8	no	—
307	C₂×C₄	—	94	128	no	—
308	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	96	yes	direct product factor
309	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
310	C₂×C₄	C₂²×C₄×D₄₇	1	16	yes	complemented
311	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
312	C₂×C₄	C₂²×D₁₈₈	1	8	yes	—
313	C₂²	—	47	16	no	—
314	C₂²	—	94	8	no	—
315	C₂²	—	94	8	no	—
316	C₂²	—	94	16	no	—
317	C₂²	—	94	16	no	—
318	C₂²	—	94	192	no	—
319	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	64	yes	direct product factor
320	C₂²	C₂×C₄²×D₄₇	1	12	yes	—
321	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	12	yes	—
322	C₂²	C₂×#13093981	1	12	yes	—
323	C₂²	C₂×C₄×C₂²⋊D₄₇	1	24	yes	—
324	C₂²	C₂×C₄×D₁₈₈	1	24	yes	—
325	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
326	C₂²	C₂³×C₄×D₄₇	1	2	yes	—
327	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
329	C₂²	C₂²×#10625350	1	2	yes	—
330	C₄	—	2	16	no	—
331	C₄	—	94	8	no	—
332	C₄	—	94	16	no	—
333	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	16	yes	direct product factor
334	C₂	—	94	16	no	—
335	C₂	C₂×C₄×(C₂×D₄₇)⋊C₄	1	24	yes	direct product factor
336	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
337	C₂	C₂³×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
338	C₂	C₂²×#13093981	1	1	yes	characteristic
339	C₂	C₂²×C₄×C₂²⋊D₄₇	1	2	yes	—
340	C₂	C₂²×C₄×D₁₈₈	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂⁵×C₄₇	C₂³
prime radical	C₂⁵×D₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂²×C₄×C₂²⋊C₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂³×C₄×Dic₄₇	C₂	semidirect
4. C₂×C₄×(C₂×D₄₇)⋊C₄	C₂	direct (N × H)
5. C₂²×C₄₇⋊#95	C₂	semidirect
6. C₂³×C₄²×C₄₇	C₂	semidirect
12. C₂³×C₄×D₄₇	C₄	semidirect
14. C₂²×(C₂×D₄₇)⋊C₄	C₄	direct (N × H)
17. C₂²×C₄×Dic₄₇	C₂²	semidirect
18. C₄×(C₂×D₄₇)⋊C₄	C₂²	direct (N × H)
19. C₂×C₄₇⋊#95	C₂²	semidirect
23. C₂²×C₄²×C₄₇	C₂²	semidirect
35. C₂³×Dic₄₇	C₂×C₄	semidirect
41. C₂²×C₄×D₄₇	C₂×C₄	semidirect
43. C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	direct (N × H)
46. C₂×C₄×Dic₄₇	C₂³	semidirect
47. C₄₇⋊#95	C₂³	semidirect
52. C₂³×C₄×C₄₇	C₂×C₄	semidirect
58. C₂×C₄²×C₄₇	C₂³	semidirect
72. C₂³×D₄₇	C₄²	semidirect
79. C₂²×C₄×C₄₇	C₂²⋊C₄	semidirect
81. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
93. C₂²×Dic₄₇	C₂²×C₄	semidirect
99. C₂×C₄×D₄₇	C₂²×C₄	semidirect
101. (C₂×D₄₇)⋊C₄	C₂²×C₄	direct (N × H)
122. C₂²×D₄₇	C₂×C₄²	semidirect
128. C₂×C₄×C₄₇	C₂×C₂²⋊C₄	semidirect
130. C₂×C₄×C₄₇	C₂³×C₄	semidirect
140. C₂×Dic₄₇	C₂³×C₄	semidirect
143. C₂²×C₄₇	C₄×C₂²⋊C₄	semidirect
159. C₂×D₄₇	C₂²×C₄²	semidirect
161. C₄×C₄₇	C₂²×C₂²⋊C₄	semidirect
167. C₂³×C₄²	D₄₇	semidirect
170. C₂×C₄₇	C₂×C₄×C₂²⋊C₄	semidirect
191. C₂²×C₄²	C₂×D₄₇	semidirect
194. C₄₇	C₂²×C₄×C₂²⋊C₄	semidirect
218. C₂³×C₄	C₄×D₄₇	semidirect
228. C₂×C₄²	C₂²×D₄₇	semidirect
264. C₂²×C₄	(C₂×D₄₇)⋊C₄	direct (N × H)
266. C₂²×C₄	C₂×C₄×D₄₇	semidirect
308. C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	direct (N × H)
310. C₂×C₄	C₂²×C₄×D₄₇	semidirect
319. C₂²	C₄×(C₂×D₄₇)⋊C₄	direct (N × H)
333. C₄	C₂²×(C₂×D₄₇)⋊C₄	direct (N × H)
335. C₂	C₂×C₄×(C₂×D₄₇)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×D₄₇	2
C₂³×(C₂×D₄₇)⋊C₄	2
C₂³×C₄×Dic₄₇	2
C₂×C₄×(C₂×D₄₇)⋊C₄	2
C₂²×C₄₇⋊#95	2
C₂³×C₄²×C₄₇	2
C₂²×C₄×C₂²⋊C₄	47

Subgroups — C22×C4×(C2×D47)⋊C4 #26374452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×(C₂×D₄₇)⋊C₄ #26374452