Subgroups — #26122127

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688989	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	4	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
10	#15688989	—	2	2	no	—
11	#15688989	C₄	1	4	yes	complemented
12	C₂×C₄₇⋊#95	—	2	1	no	—
13	C₂×C₄₇⋊#95	—	2	1	no	—
14	#15688885	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	—	2	1	no	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	complemented
20	C₂×#95×C₄₇	—	2	1	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	4	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	4	no	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄⋊Dic₄₇	—	2	4	no	—
28	C₂×C₄⋊Dic₄₇	—	2	4	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
31	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
32	C₄₇⋊#95	—	2	4	no	—
33	C₄₇⋊#95	—	2	4	no	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
43	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
44	C₂×C₄²×C₄₇	—	2	4	no	—
45	C₂×C₄²×C₄₇	—	4	4	no	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₄₇	D₄	1	2	yes	—
50	C₂×C₄²×C₄₇	D₄	1	2	yes	—
51	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
52	#95×C₄₇	—	2	4	no	—
53	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	—	2	4	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	4	no	—
58	C₂²×C₄×C₄₇	—	2	4	no	—
59	C₂²×C₄×C₄₇	—	2	4	no	—
60	C₂²×C₄×C₄₇	—	4	4	no	—
61	C₂²×C₄×C₄₇	—	4	4	no	—
62	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₄₇	#41	1	2	yes	—
77	C₂²×C₄×C₄₇	#41	1	2	yes	—
78	C₂²×Dic₄₇	—	2	4	no	—
79	C₂²×Dic₄₇	—	4	4	no	—
80	C₂²×Dic₄₇	—	4	4	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₄⋊C₄×C₄₇	—	2	4	no	—
84	C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₄⋊C₄×C₄₇	—	2	4	no	—
86	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
87	C₄²×C₄₇	—	4	8	no	—
88	C₄²×C₄₇	C₄²	1	4	yes	—
89	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
90	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
91	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
92	C₄⋊Dic₄₇	—	2	8	no	—
93	C₄⋊Dic₄₇	—	4	2	no	—
94	C₄⋊Dic₄₇	—	4	2	no	—
95	C₂×C₄₇⋊C₈	—	2	4	no	—
96	C₂×C₄₇⋊C₈	—	2	8	no	—
97	C₂×C₄₇⋊C₈	—	4	4	no	—
98	C₂×C₄₇⋊C₈	—	4	2	no	—
99	C₂×C₄₇⋊C₈	—	4	2	no	—
100	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂³×C₄₇	#121	1	2	yes	—
104	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
105	C₂³×C₄₇	#135	1	4	yes	—
106	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
107	C₂³×C₄₇	#137	1	2	yes	—
108	C₂×C₄×C₄₇	—	2	4	no	—
109	C₂×C₄×C₄₇	—	2	4	no	—
110	C₂×C₄×C₄₇	—	2	4	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	4	no	—
117	C₂×C₄×C₄₇	—	4	4	no	—
118	C₂×C₄×C₄₇	—	4	8	no	—
119	C₂×C₄×C₄₇	—	4	8	no	—
120	C₂×C₄×C₄₇	#95	1	4	yes	—
121	C₂×C₄×C₄₇	#95	1	4	yes	—
122	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
123	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₄₇	#117	1	2	yes	—
128	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₄₇	#121	1	2	yes	—
133	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
134	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#125	1	2	yes	—
137	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
139	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
140	C₂×Dic₄₇	—	4	4	no	—
141	C₂×Dic₄₇	—	4	4	no	—
142	C₂×Dic₄₇	—	4	4	no	—
143	C₂×Dic₄₇	—	8	4	no	—
144	C₂×Dic₄₇	—	8	4	no	—
145	C₄₇⋊C₈	—	4	4	no	—
146	#10850	—	47	1	no	maximal, Sylow
147	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
148	C₂²×C₄₇	#380	1	2	yes	—
149	C₂²×C₄₇	#389	1	2	yes	—
150	C₂²×C₄₇	#390	1	1	yes	characteristic
151	C₂²×C₄₇	#391	1	1	yes	characteristic
152	C₂²×C₄₇	#416	1	2	yes	—
153	C₂²×C₄₇	#416	1	2	yes	—
154	C₂²×C₄₇	#417	1	2	yes	—
155	C₂²×C₄₇	#418	1	1	yes	characteristic
156	C₂²×C₄₇	#419	1	1	yes	characteristic
157	C₂²×C₄₇	#427	1	2	yes	—
158	C₂²×C₄₇	#428	1	2	yes	—
159	C₂²×C₄₇	#463	1	4	yes	—
160	C₂²×C₄₇	#464	1	4	yes	—
161	C₂²×C₄₇	#478	1	4	yes	—
162	C₂²×C₄₇	#479	1	4	yes	—
163	C₄×C₄₇	—	2	4	no	—
164	C₄×C₄₇	—	2	4	no	—
165	C₄×C₄₇	—	4	8	no	—
166	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
167	C₄×C₄₇	#382	1	1	yes	characteristic
168	C₄×C₄₇	#384	1	1	yes	characteristic
169	C₄×C₄₇	#389	1	2	yes	—
170	C₄×C₄₇	#390	1	1	yes	characteristic
171	C₄×C₄₇	#391	1	1	yes	characteristic
172	Dic₄₇	—	8	4	no	—
173	C₂²×C₄⋊C₈	—	47	1	no	—
174	C₂×#382	—	47	1	no	—
175	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
176	C₂×#340	—	47	4	no	—
177	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
178	C₂×C₄₇	#1735	1	1	yes	characteristic
179	C₂×C₄₇	#1736	1	1	yes	characteristic
180	C₂×C₄₇	#1804	1	2	yes	—
181	C₂×C₄₇	#1805	1	2	yes	—
182	C₂×C₄₇	#1949	1	4	yes	—
183	C₂×C₄₇	#1983	1	2	yes	—
184	C₂×C₄₇	#1989	1	2	yes	—
185	C₂³×C₈	—	47	2	no	—
186	C₂²×C₄⋊C₄	—	47	2	no	—
187	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
188	C₂²×C₄²	—	2	1	no	—
189	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
190	C₂×C₄⋊C₈	—	47	4	no	—
191	C₂×C₄⋊C₈	—	94	2	no	—
192	C₂×C₄⋊C₈	—	94	2	no	—
193	#382	—	47	4	no	—
194	#382	—	94	2	no	—
195	C₄×C₄⋊C₄	—	2	2	no	—
196	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	complemented
197	C₂×#95	—	2	1	no	—
198	C₂×#95	—	94	1	no	—
199	C₂×#95	—	94	1	no	—
200	#340	—	94	8	no	—
201	C₄₇	#10850	1	1	yes	characteristic, complemented, Sylow
202	C₂³×C₄	—	2	2	no	—
203	C₂³×C₄	—	94	2	no	—
204	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
205	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
206	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
207	C₂²×C₈	—	47	4	no	—
208	C₂²×C₈	—	94	4	no	—
209	C₂²×C₈	—	94	2	no	—
210	C₂²×C₈	—	94	4	no	—
211	C₂²×C₈	—	94	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	47	4	no	—
216	C₂×C₄⋊C₄	—	94	4	no	—
217	C₂×C₄⋊C₄	—	94	4	no	—
218	C₂×C₄⋊C₄	—	94	2	no	—
219	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
220	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
221	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
222	C₂×C₄²	—	2	4	no	—
223	C₂×C₄²	—	4	4	no	—
224	C₂×C₄²	Dic₉₄	1	2	yes	—
225	C₂×C₄²	C₄×D₄₇	1	2	yes	—
226	C₂×C₄²	C₄×D₄₇	1	2	yes	—
227	C₂×C₄²	D₁₈₈	1	2	yes	—
228	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
229	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
230	C₄⋊C₈	—	94	8	no	—
231	#95	—	2	4	no	—
232	#95	—	94	4	no	—
233	#95	—	94	4	no	—
234	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	4	4	no	—
243	C₂²×C₄	—	94	4	no	—
244	C₂²×C₄	—	188	4	no	—
245	C₂²×C₄	—	188	4	no	—
246	C₂²×C₄	—	188	2	no	—
247	C₂²×C₄	—	188	2	no	—
248	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
249	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
250	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
251	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
252	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
253	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
254	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
255	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
256	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
260	C₂²×C₄	#10625350	1	2	yes	—
261	C₂²×C₄	#10625350	1	2	yes	—
262	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₈	—	94	4	no	—
265	C₂×C₈	—	94	8	no	—
266	C₂×C₈	—	188	4	no	—
267	C₂×C₈	—	188	2	no	—
268	C₂×C₈	—	188	2	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	94	8	no	—
273	C₄⋊C₄	—	188	2	no	—
274	C₄⋊C₄	—	188	2	no	—
275	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	—
276	C₄²	—	4	8	no	—
277	C₄²	C₄×Dic₄₇	1	4	yes	—
278	C₄²	Dic₄₇⋊C₄	1	4	yes	—
279	C₄²	C₄⋊Dic₄₇	1	4	yes	—
280	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
281	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
282	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
283	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
284	C₂³	#13093998	1	2	yes	—
285	C₂³	#13094003	1	2	yes	—
286	C₂³	#13094044	1	4	yes	—
287	C₂³	#13094050	1	2	yes	—
288	C₂³	#13094055	1	2	yes	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	4	8	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	8	no	—
301	C₂×C₄	—	376	4	no	—
302	C₂×C₄	—	376	4	no	—
303	C₂×C₄	—	188	4	no	—
304	C₂×C₄	—	188	4	no	—
305	C₂×C₄	—	188	4	no	—
306	C₂×C₄	C₄₇⋊#95	1	4	yes	—
307	C₂×C₄	C₄₇⋊#95	1	4	yes	—
308	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
309	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
310	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
312	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
313	C₂×C₄	#13093983	1	2	yes	—
314	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
315	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
316	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
317	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
318	C₂×C₄	#13093998	1	2	yes	—
319	C₂×C₄	#13094003	1	2	yes	—
320	C₂×C₄	#13094012	1	1	yes	characteristic
321	C₂×C₄	#13094012	1	1	yes	characteristic
322	C₂×C₄	#13094016	1	2	yes	—
323	C₂×C₄	#13094021	1	1	yes	characteristic
324	C₂×C₄	#13094024	1	2	yes	—
325	C₂×C₄	#13094024	1	1	yes	characteristic
326	C₈	—	188	4	no	—
327	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
328	C₂²	#15688983	1	2	yes	—
329	C₂²	#15689021	1	2	yes	—
330	C₂²	#15689025	1	1	yes	characteristic
331	C₂²	#15689029	1	1	yes	characteristic
332	C₂²	#15689117	1	2	yes	—
333	C₂²	#15689119	1	2	yes	—
334	C₂²	#15689122	1	2	yes	—
335	C₂²	#15689128	1	1	yes	characteristic
336	C₂²	#15689132	1	1	yes	characteristic
337	C₂²	#15689159	1	2	yes	—
338	C₂²	#15689163	1	2	yes	—
339	C₂²	#15689338	1	4	yes	—
340	C₂²	#15689345	1	4	yes	—
341	C₂²	#15689423	1	4	yes	—
342	C₂²	#15689430	1	4	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	4	8	no	—
346	C₄	—	376	4	no	—
347	C₄	C₄×C₄⋊Dic₄₇	1	2	yes	—
348	C₄	#15688989	1	1	yes	characteristic
349	C₄	#15688993	1	1	yes	characteristic
350	C₄	#15689021	1	2	yes	—
351	C₄	#15689025	1	1	yes	characteristic
352	C₄	#15689029	1	1	yes	characteristic
353	C₂	#20241618	1	1	yes	characteristic
354	C₂	#20243104	1	1	yes	characteristic
355	C₂	#20243107	1	1	yes	characteristic
356	C₂	#20243398	1	2	yes	—
357	C₂	#20243403	1	2	yes	—
358	C₂	#20244156	1	4	yes	—
359	C₂	#20244320	1	2	yes	—
360	C₂	#20244345	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#10850
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
11. #15688989	C₄	semidirect
19. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
196. C₄×C₄⋊C₄	Dic₄₇	semidirect
201. C₄₇	#10850	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688989	2
C₂×#15688885	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#10850	47