Subgroups — C₂×C₄×#13093993 #26374692

Order 12032.

8582 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093993	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₂²⋊D₄₇	C₂	1	3	yes	maximal, complemented
3	C₄×#13093993	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689002	C₂	1	3	yes	maximal, complemented
5	C₂×#15688996	C₂	1	3	yes	maximal, complemented
6	C₂×#15688979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	3	yes	maximal, complemented
8	C₂⁵×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₂²⋊D₄₇	C₂²	1	3	yes	—
10	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
11	C₂×#13093993	C₄	1	16	yes	direct product factor
12	C₂×#13093993	C₂²	1	8	yes	—
13	C₂×C₄×C₂²⋊D₄₇	—	2	24	no	—
14	C₂×C₄×C₂²⋊D₄₇	C₂²	1	24	yes	complemented
15	C₂²×Dic₄₇⋊C₄	C₂²	1	3	yes	complemented
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
19	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	complemented
20	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	complemented
21	#15689002	C₂²	1	24	yes	complemented
22	#15688996	C₂²	1	24	yes	complemented
23	#15688979	C₂²	1	8	yes	complemented
24	C₄×C₂²⋊Dic₄₇	C₂²	1	24	yes	complemented
25	C₂×C₄₇⋊#95	C₂²	1	6	yes	complemented
26	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄×C₄₇	—	2	24	no	—
28	C₂⁴×C₄×C₄₇	C₂²	1	3	yes	—
29	C₂⁴×C₄×C₄₇	C₂²	1	3	yes	—
30	C₂⁴×C₄×C₄₇	C₂²	1	8	yes	complemented
31	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
32	C₂²×C₂²⋊D₄₇	—	2	12	no	—
33	C₂²×C₂²⋊D₄₇	—	2	12	no	—
34	C₂²×C₂²⋊D₄₇	C₂×C₄	1	24	yes	complemented
35	C₂²×C₂²⋊D₄₇	C₂³	1	12	yes	—
36	C₂³×Dic₄₇	C₂³	1	3	yes	—
37	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
38	C₂³×Dic₄₇	C₂³	1	3	yes	—
39	C₂²×C₄×D₄₇	—	2	12	no	—
40	C₂²×C₄×D₄₇	C₂³	1	4	yes	complemented
41	#13093993	C₂×C₄	1	64	yes	direct product factor
42	C₄×C₂²⋊D₄₇	—	2	96	no	—
43	C₂×Dic₄₇⋊C₄	—	2	12	no	—
44	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	complemented
45	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
46	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
47	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	24	yes	complemented
48	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
49	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
51	C₂×(C₂×D₄₇)⋊C₄	—	2	12	no	—
52	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	complemented
53	C₂×C₄×Dic₄₇	—	2	12	no	—
54	C₂×C₄×Dic₄₇	C₂³	1	12	yes	complemented
55	C₄₇⋊#95	C₂³	1	24	yes	complemented
56	C₂⁵×C₄₇	—	2	12	no	—
57	C₂⁵×C₄₇	—	2	12	no	—
58	C₂⁵×C₄₇	C₂×C₄	1	8	yes	complemented
59	C₂⁵×C₄₇	C₂³	1	4	yes	—
60	C₂⁵×C₄₇	C₂³	1	3	yes	—
61	C₂³×C₄×C₄₇	—	2	128	no	—
62	C₂³×C₄×C₄₇	—	2	12	no	—
63	C₂³×C₄×C₄₇	—	2	24	no	—
64	C₂³×C₄×C₄₇	—	2	24	no	—
65	C₂³×C₄×C₄₇	—	2	96	no	—
66	C₂³×C₄×C₄₇	D₄	1	24	yes	complemented
67	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
68	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	12	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂⁴×C₄₇	—	2	32	no	—
72	C₂⁴×C₄₇	—	2	96	no	—
73	C₂⁴×C₄₇	—	2	96	no	—
74	C₂⁴×C₄₇	—	2	24	no	—
75	C₂⁴×C₄₇	—	2	12	no	—
76	C₂⁴×C₄₇	—	2	24	no	—
77	C₂⁴×C₄₇	—	2	12	no	—
78	C₂⁴×C₄₇	C₂²×C₄	1	12	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	complemented
80	C₂⁴×C₄₇	C₂×D₄	1	12	yes	—
81	C₂⁴×C₄₇	#41	1	12	yes	—
82	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
83	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
84	C₂³×D₄₇	—	2	6	no	—
85	C₂³×D₄₇	—	2	6	no	—
86	C₂³×D₄₇	C₂²×C₄	1	4	yes	complemented
87	C₂³×D₄₇	C₂⁴	1	2	yes	—
88	C₂²×C₄×C₄₇	—	2	96	no	—
89	C₂²×C₄×C₄₇	—	2	256	no	—
90	C₂²×C₄×C₄₇	—	2	24	no	—
91	C₂²×C₄×C₄₇	—	2	12	no	—
92	C₂²×C₄×C₄₇	—	2	96	no	—
93	C₂²×C₄×C₄₇	—	2	48	no	—
94	C₂²×C₄×C₄₇	—	2	48	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	48	yes	complemented
98	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
100	C₂×C₂²⋊D₄₇	—	2	96	no	—
101	C₂×C₂²⋊D₄₇	—	2	24	no	—
102	C₂×C₂²⋊D₄₇	—	2	24	no	—
103	C₂×C₂²⋊D₄₇	C₂²×C₄	1	48	yes	complemented
104	C₂²×Dic₄₇	—	2	6	no	—
105	C₂²×Dic₄₇	—	2	6	no	—
106	C₂²×Dic₄₇	—	2	6	no	—
107	C₂²×Dic₄₇	—	2	6	no	—
108	C₂²×Dic₄₇	—	2	12	no	—
109	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	complemented
110	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
111	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
112	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
113	C₂×C₄×D₄₇	—	2	24	no	—
114	C₂×C₄×D₄₇	—	4	16	no	—
115	C₂²⋊Dic₄₇	—	2	24	no	—
116	C₂²⋊Dic₄₇	—	2	24	no	—
117	C₂²⋊Dic₄₇	C₂²×C₄	1	48	yes	complemented
118	(C₂×D₄₇)⋊C₄	—	2	24	no	—
119	Dic₄₇⋊C₄	—	2	24	no	—
120	C₄×Dic₄₇	—	2	24	no	—
121	C₂³×C₄₇	—	2	32	no	—
122	C₂³×C₄₇	—	2	96	no	—
123	C₂³×C₄₇	—	2	256	no	—
124	C₂³×C₄₇	—	2	48	no	—
125	C₂³×C₄₇	—	2	96	no	—
126	C₂³×C₄₇	—	2	24	no	—
127	C₂³×C₄₇	—	2	24	no	—
128	C₂³×C₄₇	—	2	48	no	—
129	C₂³×C₄₇	—	2	12	no	—
130	C₂³×C₄₇	—	2	12	no	—
131	C₂³×C₄₇	C₄×D₄	1	48	yes	complemented
132	C₂³×C₄₇	C₂³×C₄	1	12	yes	—
133	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	12	yes	—
135	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
136	C₂³×C₄₇	C₂×#41	1	12	yes	—
137	C₂³×C₄₇	C₂×#41	1	6	yes	—
138	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	24	no	—
140	C₂²×D₄₇	—	2	6	no	—
141	C₂²×D₄₇	—	2	6	no	—
142	C₂²×D₄₇	—	4	4	no	—
143	C₂²×D₄₇	—	4	12	no	—
144	C₂²×D₄₇	C₂³×C₄	1	4	yes	complemented
145	C₂×C₄×C₄₇	—	2	96	no	—
146	C₂×C₄×C₄₇	—	2	24	no	—
147	C₂×C₄×C₄₇	—	2	12	no	—
148	C₂×C₄×C₄₇	—	2	96	no	—
149	C₂×C₄×C₄₇	#120	1	16	yes	complemented
150	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
151	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
152	C₂²⋊D₄₇	—	2	96	no	—
153	C₂×Dic₄₇	—	2	24	no	—
154	C₂×Dic₄₇	—	2	6	no	—
155	C₂×Dic₄₇	—	2	6	no	—
156	C₂×Dic₄₇	—	2	6	no	—
157	C₂×Dic₄₇	—	2	6	no	—
158	C₂×Dic₄₇	—	2	12	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	12	no	—
161	C₂×Dic₄₇	C₂³×C₄	1	12	yes	complemented
162	C₄×D₄₇	—	4	16	no	—
163	C₂×C₄×#120	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	128	no	—
165	C₂²×C₄₇	—	2	24	no	—
166	C₂²×C₄₇	—	2	12	no	—
167	C₂²×C₄₇	—	2	12	no	—
168	C₂²×C₄₇	—	2	24	no	—
169	C₂²×C₄₇	—	2	96	no	—
170	C₂²×C₄₇	C₂×C₄×D₄	1	12	yes	—
171	C₂²×C₄₇	C₂×C₄×D₄	1	24	yes	complemented
172	C₂²×C₄₇	C₂×#120	1	4	yes	—
173	C₂²×C₄₇	#525	1	12	yes	—
174	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂³×D₄	1	3	yes	—
176	C₂²×C₄₇	C₂²×#41	1	3	yes	—
177	C₂×D₄₇	—	2	12	no	—
178	C₂×D₄₇	—	4	2	no	—
179	C₂×D₄₇	—	4	6	no	—
180	C₂×D₄₇	—	4	16	no	—
181	C₄×C₄₇	—	2	12	no	—
182	C₄×C₄₇	C₂×#120	1	8	yes	complemented
183	Dic₄₇	—	2	12	no	—
184	Dic₄₇	—	4	2	no	—
185	Dic₄₇	—	4	6	no	—
186	C₂⁵×C₄	D₄₇	1	1	yes	characteristic, complemented
187	C₂²×#120	—	47	1	no	—
188	C₂²×C₄×D₄	—	47	3	no	—
189	C₄×#120	—	47	16	no	—
190	C₂×#386	—	47	3	no	—
191	C₂×#385	—	47	3	no	—
192	C₂×#379	—	47	1	no	—
193	C₂×C₄×C₂²⋊C₄	—	47	3	no	—
194	C₂×C₄₇	—	2	24	no	—
195	C₂×C₄₇	C₄×#120	1	8	yes	complemented
196	C₂×C₄₇	C₂²×C₄×D₄	1	3	yes	—
197	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
198	C₂×C₄₇	C₂×#525	1	3	yes	—
199	D₄₇	—	4	4	no	—
200	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
201	C₂³×D₄	—	47	3	no	—
202	C₂⁴×C₄	—	2	24	no	—
203	C₂⁴×C₄	—	47	1	no	—
204	C₂⁴×C₄	C₂×D₄₇	1	3	yes	—
205	C₂⁴×C₄	C₂×D₄₇	1	3	yes	—
206	C₂⁴×C₄	C₂×D₄₇	1	8	yes	complemented
207	C₂×#120	—	47	16	no	—
208	C₂×#120	—	47	8	no	—
209	C₂×C₄×D₄	—	47	24	no	—
210	C₂×C₄×D₄	—	94	24	no	—
211	C₂²×C₄⋊C₄	—	47	3	no	—
212	C₂²×C₂²⋊C₄	—	47	3	no	—
213	C₂²×C₂²⋊C₄	—	47	3	no	—
214	C₂²×C₂²⋊C₄	—	47	3	no	—
215	C₂²×C₂²⋊C₄	—	47	3	no	—
216	C₂²×C₄²	—	47	3	no	—
217	#386	—	47	24	no	—
218	#385	—	47	24	no	—
219	#379	—	47	8	no	—
220	C₄×C₂²⋊C₄	—	47	24	no	—
221	C₂×#95	—	47	6	no	—
222	C₄₇	C₂×C₄×#120	1	1	yes	characteristic, complemented, Sylow
223	C₂⁵	—	2	12	no	—
224	C₂⁵	—	2	12	no	—
225	C₂⁵	—	47	1	no	—
226	C₂⁵	C₄×D₄₇	1	8	yes	complemented
227	C₂⁵	C₂²×D₄₇	1	4	yes	—
228	C₂⁵	C₂²×D₄₇	1	3	yes	—
229	C₂²×D₄	—	47	24	no	—
230	C₂²×D₄	—	47	12	no	—
231	C₂²×D₄	—	94	12	no	—
232	C₂²×D₄	—	94	12	no	—
233	C₂³×C₄	—	2	128	no	—
234	C₂³×C₄	—	2	12	no	—
235	C₂³×C₄	—	2	24	no	—
236	C₂³×C₄	—	2	24	no	—
237	C₂³×C₄	—	2	96	no	—
238	C₂³×C₄	—	47	3	no	—
239	C₂³×C₄	—	47	3	no	—
240	C₂³×C₄	—	47	1	no	—
241	C₂³×C₄	—	47	4	no	—
242	C₂³×C₄	—	94	12	no	—
243	C₂³×C₄	C₂²⋊D₄₇	1	24	yes	complemented
244	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
245	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
246	C₂³×C₄	C₂²×D₄₇	1	12	yes	—
247	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
248	#120	—	47	64	no	—
249	C₄×D₄	—	94	96	no	—
250	C₂×C₄⋊C₄	—	47	12	no	—
251	C₂×C₄⋊C₄	—	94	12	no	—
252	C₂×C₂²⋊C₄	—	47	24	no	—
253	C₂×C₂²⋊C₄	—	47	12	no	—
254	C₂×C₂²⋊C₄	—	47	12	no	—
255	C₂×C₂²⋊C₄	—	47	12	no	—
256	C₂×C₂²⋊C₄	—	47	12	no	—
257	C₂×C₂²⋊C₄	—	94	12	no	—
258	C₂×C₂²⋊C₄	—	94	12	no	—
259	C₂×C₂²⋊C₄	—	94	12	no	—
260	C₂×C₄²	—	47	12	no	—
261	C₂×C₄²	—	94	12	no	—
262	#95	—	47	24	no	—
263	C₂⁴	—	2	32	no	—
264	C₂⁴	—	2	96	no	—
265	C₂⁴	—	2	96	no	—
266	C₂⁴	—	2	24	no	—
267	C₂⁴	—	2	12	no	—
268	C₂⁴	—	2	24	no	—
269	C₂⁴	—	2	12	no	—
270	C₂⁴	—	47	4	no	—
271	C₂⁴	—	47	2	no	—
272	C₂⁴	—	94	6	no	—
273	C₂⁴	—	94	6	no	—
274	C₂⁴	C₂×C₄×D₄₇	1	12	yes	—
275	C₂⁴	C₂×C₄×D₄₇	1	16	yes	complemented
276	C₂⁴	#10625350	1	12	yes	—
277	C₂⁴	C₂×C₂²⋊D₄₇	1	12	yes	—
278	C₂⁴	C₂³×D₄₇	1	6	yes	—
279	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
280	C₂×D₄	—	47	48	no	—
281	C₂×D₄	—	94	96	no	—
282	C₂×D₄	—	94	24	no	—
283	C₂×D₄	—	94	24	no	—
284	C₂²×C₄	—	2	96	no	—
285	C₂²×C₄	—	2	256	no	—
286	C₂²×C₄	—	2	24	no	—
287	C₂²×C₄	—	2	12	no	—
288	C₂²×C₄	—	2	96	no	—
289	C₂²×C₄	—	2	48	no	—
290	C₂²×C₄	—	2	48	no	—
291	C₂²×C₄	—	47	12	no	—
292	C₂²×C₄	—	47	6	no	—
293	C₂²×C₄	—	47	6	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	94	6	no	—
296	C₂²×C₄	—	94	6	no	—
297	C₂²×C₄	—	94	6	no	—
298	C₂²×C₄	—	94	6	no	—
299	C₂²×C₄	—	94	12	no	—
300	C₂²×C₄	—	94	24	no	—
301	C₂²×C₄	—	188	16	no	—
302	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
303	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	48	yes	complemented
305	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
306	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
307	C₄⋊C₄	—	94	24	no	—
308	C₂²⋊C₄	—	47	48	no	—
309	C₂²⋊C₄	—	94	24	no	—
310	C₂²⋊C₄	—	94	24	no	—
311	C₂²⋊C₄	—	94	24	no	—
312	C₄²	—	94	24	no	—
313	C₂³	—	2	32	no	—
314	C₂³	—	2	96	no	—
315	C₂³	—	2	256	no	—
316	C₂³	—	2	48	no	—
317	C₂³	—	2	96	no	—
318	C₂³	—	2	24	no	—
319	C₂³	—	2	48	no	—
320	C₂³	—	2	24	no	—
321	C₂³	—	2	12	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	47	4	no	—
324	C₂³	—	94	24	no	—
325	C₂³	—	94	6	no	—
326	C₂³	—	94	6	no	—
327	C₂³	—	188	4	no	—
328	C₂³	—	188	12	no	—
329	C₂³	C₄×C₂²⋊D₄₇	1	48	yes	complemented
330	C₂³	C₂²×C₄×D₄₇	1	12	yes	—
331	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
332	C₂³	C₂²×C₂²⋊D₄₇	1	12	yes	—
333	C₂³	C₂²×C₂²⋊D₄₇	1	6	yes	—
334	C₂³	C₂×#10625350	1	12	yes	—
335	C₂³	C₂×#10625350	1	6	yes	—
336	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
337	D₄	—	94	96	no	—
338	C₂×C₄	—	2	96	no	—
339	C₂×C₄	—	2	24	no	—
340	C₂×C₄	—	2	12	no	—
341	C₂×C₄	—	2	96	no	—
342	C₂×C₄	—	47	12	no	—
343	C₂×C₄	—	94	24	no	—
344	C₂×C₄	—	94	6	no	—
345	C₂×C₄	—	94	6	no	—
346	C₂×C₄	—	94	6	no	—
347	C₂×C₄	—	94	6	no	—
348	C₂×C₄	—	94	12	no	—
349	C₂×C₄	—	188	4	no	—
350	C₂×C₄	—	188	12	no	—
351	C₂×C₄	—	188	16	no	—
352	C₂×C₄	#13093993	1	16	yes	direct product factor
353	C₂×C₄	C₂²×C₂²⋊D₄₇	1	12	yes	—
354	C₂×C₄	C₂²×C₂²⋊D₄₇	1	12	yes	—
355	C₂²	—	2	128	no	—
356	C₂²	—	2	24	no	—
357	C₂²	—	2	12	no	—
358	C₂²	—	2	12	no	—
359	C₂²	—	2	24	no	—
360	C₂²	—	2	96	no	—
361	C₂²	—	94	12	no	—
362	C₂²	—	188	2	no	—
363	C₂²	—	188	6	no	—
364	C₂²	—	188	16	no	—
365	C₂²	C₂×C₄×C₂²⋊D₄₇	1	12	yes	—
366	C₂²	C₂×C₄×C₂²⋊D₄₇	1	24	yes	complemented
367	C₂²	C₂×#13093993	1	4	yes	—
368	C₂²	#15689634	1	12	yes	—
369	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
370	C₂²	C₂³×C₂²⋊D₄₇	1	3	yes	—
371	C₂²	C₂²×#10625350	1	3	yes	—
372	C₄	—	2	12	no	—
373	C₄	—	94	12	no	—
374	C₄	—	188	2	no	—
375	C₄	—	188	6	no	—
376	C₄	C₂×#13093993	1	8	yes	direct product factor
377	C₂	—	2	24	no	—
378	C₂	—	188	4	no	—
379	C₂	C₄×#13093993	1	8	yes	direct product factor
380	C₂	C₂²×C₄×C₂²⋊D₄₇	1	3	yes	—
381	C₂	C₂²×#13093993	1	1	yes	characteristic
382	C₂	C₂×#15689634	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂⁵×C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂²×#13093993	C₂
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂⁵×C₄	D₄₇
hypocenter	C₄₇	C₂×C₄×#120
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₂²⋊D₄₇	C₂	semidirect
3. C₄×#13093993	C₂	direct (N × H)
4. C₂×#15689002	C₂	semidirect
5. C₂×#15688996	C₂	semidirect
6. C₂×#15688979	C₂	semidirect
7. C₂×C₄×C₂²⋊Dic₄₇	C₂	semidirect
8. C₂⁵×C₄×C₄₇	C₂	semidirect
10. C₂³×C₄×D₄₇	C₂²	semidirect
11. C₂×#13093993	C₄	direct (N × H)
14. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
15. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
19. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
20. C₂²×C₄×Dic₄₇	C₂²	semidirect
21. #15689002	C₂²	semidirect
22. #15688996	C₂²	semidirect
23. #15688979	C₂²	semidirect
24. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
25. C₂×C₄₇⋊#95	C₂²	semidirect
30. C₂⁴×C₄×C₄₇	C₂²	semidirect
34. C₂²×C₂²⋊D₄₇	C₂×C₄	semidirect
40. C₂²×C₄×D₄₇	C₂³	semidirect
41. #13093993	C₂×C₄	direct (N × H)
44. C₂×Dic₄₇⋊C₄	C₂³	semidirect
47. C₂×C₂²⋊Dic₄₇	C₂×C₄	semidirect
52. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
54. C₂×C₄×Dic₄₇	C₂³	semidirect
55. C₄₇⋊#95	C₂³	semidirect
58. C₂⁵×C₄₇	C₂×C₄	semidirect
66. C₂³×C₄×C₄₇	D₄	semidirect
79. C₂⁴×C₄₇	C₂²×C₄	semidirect
86. C₂³×D₄₇	C₂²×C₄	semidirect
97. C₂²×C₄×C₄₇	C₂×D₄	semidirect
103. C₂×C₂²⋊D₄₇	C₂²×C₄	semidirect
109. C₂²×Dic₄₇	C₂²×C₄	semidirect
117. C₂²⋊Dic₄₇	C₂²×C₄	semidirect
131. C₂³×C₄₇	C₄×D₄	semidirect
144. C₂²×D₄₇	C₂³×C₄	semidirect
149. C₂×C₄×C₄₇	#120	semidirect
161. C₂×Dic₄₇	C₂³×C₄	semidirect
171. C₂²×C₄₇	C₂×C₄×D₄	semidirect
182. C₄×C₄₇	C₂×#120	semidirect
186. C₂⁵×C₄	D₄₇	semidirect
195. C₂×C₄₇	C₄×#120	semidirect
206. C₂⁴×C₄	C₂×D₄₇	semidirect
222. C₄₇	C₂×C₄×#120	semidirect
226. C₂⁵	C₄×D₄₇	semidirect
243. C₂³×C₄	C₂²⋊D₄₇	semidirect
275. C₂⁴	C₂×C₄×D₄₇	semidirect
304. C₂²×C₄	C₂×C₂²⋊D₄₇	semidirect
329. C₂³	C₄×C₂²⋊D₄₇	semidirect
352. C₂×C₄	#13093993	direct (N × H)
366. C₂²	C₂×C₄×C₂²⋊D₄₇	semidirect
376. C₄	C₂×#13093993	direct (N × H)
379. C₂	C₄×#13093993	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×#13093993	2
C₂²×C₄×C₂²⋊D₄₇	2
C₄×#13093993	2
C₂×#15689002	2
C₂×#15688996	2
C₂×#15688979	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂⁵×C₄×C₄₇	2
C₂×C₄×#120	47

Subgroups — C2×C4×#13093993 #26374692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13093993 #26374692