Subgroups — #26106274

Order 12032.

850 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	#20241267	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093983	—	2	1	no	—
6	#15689176	—	2	2	no	—
7	#15689176	C₄	1	4	yes	complemented
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
11	#15688993	C₄	1	2	yes	complemented
12	#15688989	—	2	1	no	—
13	#15688983	—	2	1	no	—
14	#15688983	C₂²	1	2	yes	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	complemented
17	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
18	C₂²×C₄²×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	complemented
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	#13093983	—	4	2	no	—
25	#13093983	—	4	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
29	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄×Dic₄₇	—	2	2	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
34	C₄×C₄₇⋊C₈	—	2	4	no	—
35	C₄₇⋊#95	—	2	2	no	—
36	C₄₇⋊#95	—	2	2	no	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄²×C₄₇	—	2	4	no	—
44	C₂×C₄²×C₄₇	—	4	2	no	—
45	C₂×C₄²×C₄₇	—	4	2	no	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	D₄	1	2	yes	—
53	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
54	#95×C₄₇	—	2	2	no	—
55	#95×C₄₇	C₂×C₄	1	4	yes	—
56	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	—	2	4	no	—
58	C₂²×C₄×C₄₇	—	2	8	no	—
59	C₂²×C₄×C₄₇	—	2	4	no	—
60	C₂²×C₄×C₄₇	—	4	2	no	—
61	C₂²×C₄×C₄₇	—	4	4	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	D₈	1	2	yes	—
73	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
82	C₂²×Dic₄₇	—	2	4	no	—
83	C₄⋊C₄×C₄₇	—	2	16	no	—
84	C₄²×C₄₇	—	4	8	no	—
85	C₄²×C₄₇	C₄²	1	2	yes	—
86	C₄²×C₄₇	C₄²	1	2	yes	—
87	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
88	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
89	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
90	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
91	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
92	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₂²⋊Dic₄₇	—	4	2	no	—
94	C₂²⋊Dic₄₇	—	4	2	no	—
95	C₄⋊Dic₄₇	—	4	4	no	—
96	C₄⋊Dic₄₇	—	4	4	no	—
97	C₄⋊Dic₄₇	—	4	4	no	—
98	C₄×Dic₄₇	—	4	4	no	—
99	C₂×C₄₇⋊C₈	—	2	4	no	—
100	C₂×C₄₇⋊C₈	—	4	4	no	—
101	C₂³×C₄₇	—	2	2	no	—
102	C₂³×C₄₇	—	2	2	no	—
103	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
107	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
108	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
109	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
110	C₂×C₄×C₄₇	—	2	2	no	—
111	C₂×C₄×C₄₇	—	2	2	no	—
112	C₂×C₄×C₄₇	—	2	2	no	—
113	C₂×C₄×C₄₇	—	2	4	no	—
114	C₂×C₄×C₄₇	—	2	4	no	—
115	C₂×C₄×C₄₇	—	2	8	no	—
116	C₂×C₄×C₄₇	—	4	1	no	—
117	C₂×C₄×C₄₇	—	4	1	no	—
118	C₂×C₄×C₄₇	—	4	1	no	—
119	C₂×C₄×C₄₇	—	4	1	no	—
120	C₂×C₄×C₄₇	—	4	4	no	—
121	C₂×C₄×C₄₇	—	4	8	no	—
122	C₂×C₄×C₄₇	—	4	8	no	—
123	C₂×C₄×C₄₇	—	4	4	no	—
124	C₂×C₄×C₄₇	#95	1	2	yes	—
125	C₂×C₄×C₄₇	#95	1	2	yes	—
126	C₂×C₄×C₄₇	#95	1	2	yes	—
127	C₂×C₄×C₄₇	#95	1	2	yes	—
128	C₂×C₄×C₄₇	#102	1	2	yes	—
129	C₂×C₄×C₄₇	#102	1	2	yes	—
130	C₂×C₄×C₄₇	#102	1	4	yes	—
131	C₂×C₄×C₄₇	#103	1	2	yes	—
132	C₂×C₄×C₄₇	#103	1	2	yes	—
133	C₂×C₄×C₄₇	#103	1	4	yes	—
134	C₂×C₄×C₄₇	#104	1	4	yes	—
135	C₂×C₄×C₄₇	#106	1	4	yes	—
136	C₂×C₄×C₄₇	#107	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×Dic₄₇	—	4	4	no	—
142	C₂×Dic₄₇	—	4	4	no	—
143	C₂×Dic₄₇	—	4	4	no	—
144	C₄₇⋊C₈	—	4	4	no	—
145	#8014	—	47	1	no	maximal, Sylow
146	C₂²×C₄₇	—	2	1	no	—
147	C₂²×C₄₇	—	2	1	no	—
148	C₂²×C₄₇	—	2	1	no	—
149	C₂²×C₄₇	—	2	1	no	—
150	C₂²×C₄₇	—	2	2	no	—
151	C₂²×C₄₇	—	2	2	no	—
152	C₂²×C₄₇	—	2	2	no	—
153	C₂²×C₄₇	—	2	2	no	—
154	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
155	C₂²×C₄₇	#410	1	2	yes	—
156	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
157	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
158	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
159	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×#104	1	2	yes	—
161	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
163	C₄×C₄₇	—	2	2	no	—
164	C₄×C₄₇	—	2	1	no	—
165	C₄×C₄₇	—	2	1	no	—
166	C₄×C₄₇	—	2	1	no	—
167	C₄×C₄₇	—	2	1	no	—
168	C₄×C₄₇	—	4	8	no	—
169	C₄×C₄₇	#339	1	4	yes	—
170	C₄×C₄₇	#340	1	4	yes	—
171	C₄×C₄₇	#340	1	4	yes	—
172	Dic₄₇	—	8	4	no	—
173	C₂×#431	—	47	1	no	—
174	#2285	—	47	1	no	—
175	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
176	#1294	—	47	4	no	—
177	C₂×C₄₇	—	2	1	no	—
178	C₂×C₄₇	—	2	1	no	—
179	C₂×C₄₇	—	2	1	no	—
180	C₂×C₄₇	—	2	1	no	—
181	C₂×C₄₇	#1502	1	2	yes	—
182	C₂×C₄₇	#1503	1	2	yes	—
183	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
184	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
185	C₂×C₄₇	#1740	1	1	yes	characteristic
186	C₂×#117	—	94	1	no	—
187	C₂²×C₄⋊C₄	—	2	1	no	—
188	C₂²×C₄²	—	2	1	no	—
189	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
190	#431	—	47	4	no	—
191	#431	—	94	2	no	—
192	C₂×C₄⋊C₈	—	94	1	no	—
193	C₂×C₂²⋊C₈	—	47	2	no	—
194	C₂×C₄×C₈	—	94	1	no	—
195	#384	—	47	2	no	—
196	#382	—	94	1	no	—
197	#380	—	47	2	no	—
198	#380	—	94	1	no	—
199	C₄×C₄⋊C₄	—	2	2	no	—
200	C₄×C₄⋊C₄	—	47	2	no	—
201	C₄×C₄⋊C₄	—	94	1	no	—
202	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	complemented
203	C₂×#95	C₂×D₄₇	1	2	yes	—
204	C₄₇	#8014	1	1	yes	characteristic, complemented, Sylow
205	C₂³×C₄	—	2	2	no	—
206	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
207	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
208	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
209	C₂²×C₈	—	94	2	no	—
210	#117	—	188	2	no	—
211	#117	—	188	2	no	—
212	C₂×C₄⋊C₄	—	2	8	no	—
213	C₂×C₄⋊C₄	—	2	4	no	—
214	C₂×C₄⋊C₄	—	47	4	no	—
215	C₂×C₄⋊C₄	—	94	2	no	—
216	C₂×C₄⋊C₄	—	94	2	no	—
217	C₂×C₂²⋊C₄	—	94	2	no	—
218	C₂×C₄²	—	2	4	no	—
219	C₂×C₄²	—	4	2	no	—
220	C₂×C₄²	—	4	2	no	—
221	C₂×C₄²	—	94	2	no	—
222	C₂×C₄²	Dic₉₄	1	2	yes	—
223	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₄₇	1	2	yes	—
226	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
227	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
229	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
230	C₄⋊C₈	—	94	4	no	—
231	C₂²⋊C₈	—	47	4	no	—
232	C₂²⋊C₈	—	94	2	no	—
233	C₄×C₈	—	94	4	no	—
234	#95	—	2	2	no	—
235	#95	—	94	2	no	—
236	#95	—	94	2	no	—
237	#95	C₂×Dic₄₇	1	4	yes	—
238	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	—	4	4	no	—
244	C₂²×C₄	—	4	2	no	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	—	94	4	no	—
247	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
248	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
249	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	#10625334	1	2	yes	—
254	C₂²×C₄	#10625335	1	2	yes	—
255	C₂²×C₄	#10625336	1	2	yes	—
256	C₂²×C₄	#10625337	1	2	yes	—
257	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
258	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
259	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
263	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₈	—	94	4	no	—
266	C₂×C₈	—	188	4	no	—
267	C₄⋊C₄	—	2	16	no	—
268	C₄⋊C₄	—	188	4	no	—
269	C₄⋊C₄	—	188	4	no	—
270	C₄⋊C₄	—	188	4	no	—
271	C₂²⋊C₄	—	188	2	no	—
272	C₂²⋊C₄	—	188	2	no	—
273	C₄²	—	4	8	no	—
274	C₄²	—	188	4	no	—
275	C₄²	C₄×Dic₄₇	1	2	yes	—
276	C₄²	C₄×Dic₄₇	1	2	yes	—
277	C₄²	Dic₄₇⋊C₄	1	2	yes	—
278	C₄²	Dic₄₇⋊C₄	1	2	yes	—
279	C₄²	C₄⋊Dic₄₇	1	2	yes	—
280	C₄²	C₄⋊Dic₄₇	1	2	yes	—
281	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
282	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
286	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
287	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
288	C₂³	C₂×#10625334	1	1	yes	characteristic
289	C₂³	C₂×#10625336	1	1	yes	characteristic
290	C₂³	C₂×#10625335	1	1	yes	characteristic
291	C₂³	C₂×#10625337	1	1	yes	characteristic
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	4	1	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	188	4	no	—
307	C₂×C₄	—	188	4	no	—
308	C₂×C₄	—	188	4	no	—
309	C₂×C₄	C₄₇⋊#95	1	2	yes	—
310	C₂×C₄	C₄₇⋊#95	1	2	yes	—
311	C₂×C₄	C₄₇⋊#95	1	2	yes	—
312	C₂×C₄	C₄₇⋊#95	1	2	yes	—
313	C₂×C₄	#13093944	1	2	yes	—
314	C₂×C₄	#13093944	1	2	yes	—
315	C₂×C₄	#13093945	1	4	yes	—
316	C₂×C₄	#13093947	1	2	yes	—
317	C₂×C₄	#13093947	1	2	yes	—
318	C₂×C₄	#13093948	1	4	yes	—
319	C₂×C₄	#13093952	1	4	yes	—
320	C₂×C₄	#13093955	1	4	yes	—
321	C₂×C₄	#13093957	1	4	yes	—
322	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
326	C₈	—	188	4	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
336	C₂²	#15689096	1	2	yes	—
337	C₂²	C₂×#13093944	1	1	yes	characteristic
338	C₂²	C₂×#13093945	1	1	yes	characteristic
339	C₂²	C₂×#13093947	1	1	yes	characteristic
340	C₂²	C₂×#13093948	1	1	yes	characteristic
341	C₂²	C₂×#13093952	1	2	yes	—
342	C₂²	C₂×#13093955	1	1	yes	characteristic
343	C₂²	C₂×#13093957	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	4	8	no	—
350	C₄	—	376	4	no	—
351	C₄	#15688883	1	4	yes	—
352	C₄	#15688885	1	4	yes	—
353	C₄	#15688885	1	4	yes	—
354	C₂	—	2	1	no	—
355	C₂	—	2	1	no	—
356	C₂	—	2	1	no	—
357	C₂	—	2	1	no	—
358	C₂	#20241882	1	2	yes	—
359	C₂	#20241886	1	2	yes	—
360	C₂	C₂×#15688883	1	1	yes	characteristic
361	C₂	C₂×#15688885	1	1	yes	characteristic
362	C₂	#20243120	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#8014
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. #15689176	C₄	semidirect
11. #15688993	C₄	semidirect
16. C₄×C₄⋊Dic₄₇	C₄	semidirect
21. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
202. C₄×C₄⋊C₄	Dic₄₇	semidirect
204. C₄₇	#8014	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
#20245795	2
#20241267	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#8014	47