Subgroups — #26122064

Order 12032.

1174 conjugacy classes of subgroups.

The subgroup lattice has 356 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×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688877	C₂	1	4	yes	maximal
4	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
12	C₄²×Dic₄₇	—	2	2	no	—
13	C₄²×Dic₄₇	—	2	2	no	—
14	#15688877	—	2	8	no	—
15	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
18	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
19	C₂×C₄⋊C₈×C₄₇	C₄	1	4	yes	complemented
20	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
21	C₂²×C₄₇⋊C₈	—	2	4	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	4	no	—
25	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
26	C₂×C₄×Dic₄₇	—	2	4	no	—
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	—	2	2	no	—
31	C₂×C₄×Dic₄₇	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	8	no	—
34	C₂×C₄×Dic₄₇	C₈	1	8	yes	complemented
35	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
36	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
37	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₇	—	2	4	no	—
42	C₂²×C₈×C₄₇	—	2	2	no	—
43	C₂²×C₈×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₄₇	D₄	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	C₄⋊C₈×C₄₇	—	2	8	no	—
53	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₄₇	—	2	4	no	—
55	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
56	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
57	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
62	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
63	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
71	C₂²×C₄×C₄₇	#41	1	2	yes	—
72	C₂²×C₄×C₄₇	#41	1	2	yes	—
73	C₂²×Dic₄₇	—	2	4	no	—
74	C₂²×Dic₄₇	—	2	4	no	—
75	C₂²×Dic₄₇	—	2	4	no	—
76	C₂²×Dic₄₇	—	2	4	no	—
77	C₂²×Dic₄₇	C₄⋊C₄	1	8	yes	—
78	C₂²×Dic₄₇	C₂×C₈	1	8	yes	—
79	C₂²×Dic₄₇	M₁₆	1	8	yes	—
80	C₂×C₈×C₄₇	—	2	4	no	—
81	C₂×C₈×C₄₇	—	2	8	no	—
82	C₂×C₈×C₄₇	—	4	4	no	—
83	C₂×C₈×C₄₇	—	4	2	no	—
84	C₂×C₈×C₄₇	—	4	2	no	—
85	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
86	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
87	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
88	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
89	C₄×Dic₄₇	—	2	16	no	—
90	C₄×Dic₄₇	—	2	16	no	—
91	C₄×Dic₄₇	—	2	4	no	—
92	C₄×Dic₄₇	—	2	4	no	—
93	C₄×Dic₄₇	—	2	4	no	—
94	C₄×Dic₄₇	—	2	4	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×C₄²	1	1	yes	characteristic
101	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
103	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂³×C₄₇	#117	1	2	yes	—
105	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
106	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
107	C₂³×C₄₇	C₂×M₁₆	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	#95	1	4	yes	—
112	C₂×C₄×C₄₇	#95	1	4	yes	—
113	C₂×C₄×C₄₇	C₄×C₈	1	4	yes	—
114	C₂×C₄×C₄₇	#97	1	4	yes	—
115	C₂×C₄×C₄₇	C₂²⋊C₈	1	8	yes	—
116	C₂×C₄×C₄₇	C₄⋊C₈	1	8	yes	—
117	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
124	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₄₇	#121	1	2	yes	—
126	C₂×C₄×C₄₇	#121	1	2	yes	—
127	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
128	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
131	C₂×C₄×C₄₇	#125	1	2	yes	—
132	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
135	C₂×Dic₄₇	—	2	8	no	—
136	C₂×Dic₄₇	—	2	8	no	—
137	C₂×Dic₄₇	—	2	8	no	—
138	C₂×Dic₄₇	—	2	8	no	—
139	C₂×Dic₄₇	—	2	8	no	—
140	C₂×Dic₄₇	—	2	8	no	—
141	C₂×Dic₄₇	C₄⋊C₈	1	16	yes	complemented
142	C₈×C₄₇	—	4	4	no	—
143	C₄₇⋊C₈	—	4	4	no	—
144	#10832	—	47	1	no	maximal, Sylow
145	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
146	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
147	C₂²×C₄₇	#380	1	2	yes	—
148	C₂²×C₄₇	#382	1	1	yes	characteristic
149	C₂²×C₄₇	#384	1	1	yes	characteristic
150	C₂²×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
151	C₂²×C₄₇	C₂×#97	1	1	yes	characteristic
152	C₂²×C₄₇	C₄×M₁₆	1	2	yes	—
153	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
154	C₂²×C₄₇	#407	1	2	yes	—
155	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
156	C₂²×C₄₇	C₂×C₄⋊C₈	1	2	yes	—
157	C₂²×C₄₇	#423	1	4	yes	—
158	C₂²×C₄₇	#423	1	2	yes	—
159	C₂²×C₄₇	#431	1	4	yes	—
160	C₂²×C₄₇	#432	1	4	yes	—
161	C₄×C₄₇	—	2	4	no	—
162	C₄×C₄₇	#336	1	8	yes	complemented
163	C₄×C₄₇	#389	1	2	yes	—
164	C₄×C₄₇	#389	1	2	yes	—
165	C₄×C₄₇	#390	1	1	yes	characteristic
166	C₄×C₄₇	#390	1	1	yes	characteristic
167	C₄×C₄₇	#391	1	1	yes	characteristic
168	C₄×C₄₇	#391	1	1	yes	characteristic
169	Dic₄₇	—	2	16	no	—
170	C₂²×C₄⋊C₈	—	47	1	no	—
171	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
172	C₂×C₄³	—	47	1	no	—
173	C₂×#336	—	47	4	no	—
174	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
175	C₂×C₄₇	C₂×#336	1	1	yes	characteristic
176	C₂×C₄₇	#1728	1	1	yes	characteristic
177	C₂×C₄₇	C₄×C₄⋊C₈	1	2	yes	—
178	C₂×C₄₇	#1767	1	2	yes	—
179	C₂×C₄₇	#1797	1	4	yes	—
180	C₂×C₄₇	#1831	1	2	yes	—
181	C₂×C₄₇	#1842	1	2	yes	—
182	C₂³×C₈	—	47	2	no	—
183	C₂³×C₈	C₂×D₄₇	1	2	yes	—
184	C₂²×C₄²	—	47	2	no	—
185	C₂²×C₄²	—	47	2	no	—
186	C₂²×C₄²	—	47	2	no	—
187	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
188	C₂×C₄⋊C₈	—	2	2	no	—
189	C₂×C₄⋊C₈	—	2	2	no	—
190	C₂×C₄⋊C₈	—	47	4	no	—
191	C₂×C₄⋊C₈	—	94	2	no	—
192	C₂×C₄⋊C₈	—	94	2	no	—
193	C₂×C₄⋊C₈	Dic₄₇	1	4	yes	complemented
194	C₄³	—	94	2	no	—
195	C₄³	—	94	2	no	—
196	#336	—	94	8	no	—
197	C₄₇	#10832	1	1	yes	characteristic, complemented, Sylow
198	C₂³×C₄	—	47	4	no	—
199	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
200	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
201	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	47	4	no	—
207	C₂²×C₈	—	94	2	no	—
208	C₂²×C₈	—	94	4	no	—
209	C₂²×C₈	—	94	4	no	—
210	C₂²×C₈	—	94	2	no	—
211	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
212	C₂×C₄²	—	47	8	no	—
213	C₂×C₄²	—	47	4	no	—
214	C₂×C₄²	—	47	4	no	—
215	C₂×C₄²	—	94	8	no	—
216	C₂×C₄²	—	94	4	no	—
217	C₂×C₄²	—	94	4	no	—
218	C₂×C₄²	—	94	4	no	—
219	C₂×C₄²	—	94	2	no	—
220	C₂×C₄²	—	94	2	no	—
221	C₂×C₄²	—	94	2	no	—
222	C₂×C₄²	—	94	2	no	—
223	C₂×C₄²	Dic₉₄	1	2	yes	—
224	C₂×C₄²	C₄×D₄₇	1	2	yes	—
225	C₂×C₄²	D₁₈₈	1	2	yes	—
226	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
227	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
228	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
229	C₄⋊C₈	—	2	8	no	—
230	C₄⋊C₈	—	94	8	no	—
231	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	47	8	no	—
234	C₂²×C₄	—	47	8	no	—
235	C₂²×C₄	—	47	8	no	—
236	C₂²×C₄	—	94	4	no	—
237	C₂²×C₄	—	94	4	no	—
238	C₂²×C₄	—	94	4	no	—
239	C₂²×C₄	—	94	4	no	—
240	C₂²×C₄	C₈×D₄₇	1	4	yes	—
241	C₂²×C₄	#10625324	1	4	yes	—
242	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
243	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
244	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
245	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
246	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
247	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
248	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
249	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
251	C₂²×C₄	D₄×D₄₇	1	2	yes	—
252	C₂²×C₄	#10625352	1	2	yes	—
253	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
254	C₂²×C₄	#10625354	1	2	yes	—
255	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	8	no	—
260	C₂×C₈	—	4	4	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₂×C₈	—	94	4	no	—
264	C₂×C₈	—	94	8	no	—
265	C₂×C₈	—	188	4	no	—
266	C₂×C₈	—	188	2	no	—
267	C₂×C₈	—	188	2	no	—
268	C₄²	—	94	16	no	—
269	C₄²	—	94	16	no	—
270	C₄²	—	94	4	no	—
271	C₄²	—	94	4	no	—
272	C₄²	—	94	4	no	—
273	C₄²	—	94	4	no	—
274	C₄²	Dic₄₇⋊C₄	1	4	yes	—
275	C₄²	C₄⋊Dic₄₇	1	4	yes	—
276	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
277	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
278	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
279	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
280	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
281	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
282	C₂³	#13093982	1	2	yes	—
283	C₂³	C₂×C₈×D₄₇	1	2	yes	—
284	C₂³	M₁₆×D₄₇	1	4	yes	—
285	C₂³	C₂×#10625324	1	2	yes	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	47	16	no	—
290	C₂×C₄	—	94	8	no	—
291	C₂×C₄	—	94	8	no	—
292	C₂×C₄	—	94	8	no	—
293	C₂×C₄	—	94	8	no	—
294	C₂×C₄	—	94	8	no	—
295	C₂×C₄	—	94	8	no	—
296	C₂×C₄	C₄₇⋊#95	1	4	yes	—
297	C₂×C₄	C₄₇⋊#95	1	4	yes	—
298	C₂×C₄	C₈×Dic₄₇	1	4	yes	—
299	C₂×C₄	#13093934	1	4	yes	—
300	C₂×C₄	(C₂×D₄₇)⋊C₈	1	8	yes	—
301	C₂×C₄	Dic₄₇⋊C₈	1	8	yes	—
302	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
303	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
304	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
305	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
306	C₂×C₄	#13093986	1	2	yes	—
307	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
308	C₂×C₄	#13093989	1	2	yes	—
309	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
310	C₂×C₄	#13093995	1	2	yes	—
311	C₂×C₄	#13093999	1	2	yes	—
312	C₂×C₄	#13094000	1	2	yes	—
313	C₂×C₄	#13094004	1	2	yes	—
314	C₂×C₄	#13094011	1	1	yes	characteristic
315	C₂×C₄	#13094013	1	1	yes	characteristic
316	C₂×C₄	#13094015	1	2	yes	—
317	C₂×C₄	#13094020	1	1	yes	characteristic
318	C₂×C₄	#13094022	1	1	yes	characteristic
319	C₂×C₄	#13094023	1	2	yes	—
320	C₈	—	4	4	no	—
321	C₈	—	188	4	no	—
322	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
323	C₂²	C₄⋊C₄×Dic₄₇	1	2	yes	—
324	C₂²	#15688980	1	2	yes	—
325	C₂²	#15688988	1	1	yes	characteristic
326	C₂²	#15688992	1	1	yes	characteristic
327	C₂²	C₂×C₈×Dic₄₇	1	1	yes	characteristic
328	C₂²	C₂×#13093934	1	1	yes	characteristic
329	C₂²	M₁₆×Dic₄₇	1	2	yes	—
330	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	2	yes	—
331	C₂²	#15689086	1	2	yes	—
332	C₂²	C₄⋊C₈×D₄₇	1	4	yes	—
333	C₂²	C₂×Dic₄₇⋊C₈	1	2	yes	—
334	C₂²	#15689145	1	4	yes	—
335	C₂²	#15689146	1	2	yes	—
336	C₂²	#15689175	1	4	yes	—
337	C₂²	#15689179	1	4	yes	—
338	C₄	—	2	4	no	—
339	C₄	—	94	16	no	—
340	C₄	#15688877	1	8	yes	complemented
341	C₄	#15689019	1	2	yes	—
342	C₄	#15689022	1	2	yes	—
343	C₄	#15689024	1	1	yes	characteristic
344	C₄	#15689026	1	1	yes	characteristic
345	C₄	#15689028	1	1	yes	characteristic
346	C₄	#15689030	1	1	yes	characteristic
347	C₂	#20241617	1	1	yes	characteristic
348	C₂	C₂×#15688877	1	1	yes	characteristic
349	C₂	#20243081	1	1	yes	characteristic
350	C₂	C₄⋊C₈×Dic₄₇	1	2	yes	—
351	C₂	#20243243	1	2	yes	—
352	C₂	#20243365	1	4	yes	—
353	C₂	#20243504	1	2	yes	—
354	C₂	#20243539	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂×C₄×C₈
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#10832
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
11. C₂×C₄⋊(C₄₇⋊C₈)	C₄	semidirect
19. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
34. C₂×C₄×Dic₄₇	C₈	semidirect
141. C₂×Dic₄₇	C₄⋊C₈	semidirect
162. C₄×C₄₇	#336	semidirect
193. C₂×C₄⋊C₈	Dic₄₇	semidirect
197. C₄₇	#10832	semidirect
340. C₄	#15688877	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×C₄²×Dic₄₇	2
C₂×#15688877	2
C₂²×C₄⋊C₈×C₄₇	2
#10832	47