Subgroups — C₂×#20246281 #26375541

Order 12032.

2790 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246281	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15689022	C₂	1	2	yes	maximal, complemented
3	C₂×#15689016	C₂	1	4	yes	maximal
4	C₂×#15688991	C₂	1	2	yes	maximal, complemented
5	C₂×#15688983	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
12	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
16	#15689022	C₂²	1	16	yes	complemented
17	#15689016	C₂²	1	32	yes	—
18	#15688991	C₂²	1	16	yes	complemented
19	#15688983	C₂²	1	8	yes	—
20	C₄⋊C₄×Dic₄₇	C₂²	1	16	yes	complemented
21	C₄×C₄⋊Dic₄₇	C₂²	1	16	yes	complemented
22	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	—
23	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
24	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
25	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
26	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
27	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
28	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₄	1	16	yes	complemented
30	C₂×#117×C₄₇	C₂²	1	8	yes	—
31	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
35	C₂³×Dic₄₇	C₂³	1	2	yes	—
36	C₂³×Dic₄₇	C₂³	1	4	yes	—
37	C₂³×Dic₄₇	C₂³	1	2	yes	—
38	C₂×C₄⋊Dic₄₇	—	2	8	no	—
39	C₂×C₄⋊Dic₄₇	—	2	16	no	—
40	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
41	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
42	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
43	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
44	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
45	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
46	C₂×C₄×Dic₄₇	—	2	8	no	—
47	C₂×C₄×Dic₄₇	—	4	8	no	—
48	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
49	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
50	C₄₇⋊#95	C₂³	1	4	yes	—
51	C₄₇⋊#95	C₂³	1	4	yes	—
52	C₄₇⋊#95	C₂³	1	8	yes	—
53	C₄₇⋊#95	C₂³	1	16	yes	—
54	C₄₇⋊#95	C₂³	1	16	yes	—
55	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	—	2	8	no	—
57	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	#117×C₄₇	C₂×C₄	1	64	yes	complemented
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
69	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
78	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	8	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	32	no	—
84	C₂²×C₄×C₄₇	—	2	16	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	#41	1	8	yes	—
91	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
95	C₂²×Dic₄₇	—	2	4	no	—
96	C₂²×Dic₄₇	—	2	4	no	—
97	C₂²×Dic₄₇	—	2	4	no	—
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₂²×Dic₄₇	—	2	8	no	—
100	C₂²×Dic₄₇	—	2	8	no	—
101	C₂²×Dic₄₇	—	2	8	no	—
102	C₂²×Dic₄₇	—	2	4	no	—
103	C₂²×Dic₄₇	#41	1	8	yes	—
104	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
105	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
106	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
107	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
108	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
109	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	—
110	C₄²×C₄₇	C₂²×C₄	1	32	yes	—
111	C₂²⋊Dic₄₇	—	2	16	no	—
112	C₂²⋊Dic₄₇	—	4	8	no	—
113	C₄⋊Dic₄₇	—	2	16	no	—
114	C₄⋊Dic₄₇	—	2	32	no	—
115	C₄×Dic₄₇	—	2	16	no	—
116	C₄×Dic₄₇	—	4	16	no	—
117	C₂³×C₄₇	—	2	8	no	—
118	C₂³×C₄₇	—	2	8	no	—
119	C₂³×C₄₇	—	2	8	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	4	8	no	—
125	C₂³×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
127	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
128	C₂³×C₄₇	C₂×#41	1	4	yes	—
129	C₂³×C₄₇	C₂×#41	1	4	yes	—
130	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
131	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
132	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
133	C₂×C₄×C₄₇	—	2	8	no	—
134	C₂×C₄×C₄₇	—	2	16	no	—
135	C₂×C₄×C₄₇	—	2	16	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	32	no	—
141	C₂×C₄×C₄₇	#117	1	16	yes	—
142	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
147	C₂×Dic₄₇	—	2	16	no	—
148	C₂×Dic₄₇	—	2	4	no	—
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	2	4	no	—
151	C₂×Dic₄₇	—	2	8	no	—
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	4	16	no	—
157	C₂×Dic₄₇	—	4	8	no	—
158	C₂×Dic₄₇	C₂×#41	1	8	yes	—
159	C₂×#2347	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	4	16	no	—
164	C₂²×C₄₇	—	4	4	no	—
165	C₂²×C₄₇	—	4	4	no	—
166	C₂²×C₄₇	C₂×#117	1	4	yes	—
167	C₂²×C₄₇	C₄×#41	1	4	yes	—
168	C₂²×C₄₇	#520	1	4	yes	—
169	C₂²×C₄₇	#553	1	8	yes	—
170	C₂²×C₄₇	#556	1	8	yes	—
171	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
172	C₂²×C₄₇	C₂²×#41	1	2	yes	—
173	C₂²×C₄₇	C₂²×#41	1	2	yes	—
174	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
176	C₄×C₄₇	—	2	4	no	—
177	C₄×C₄₇	—	2	8	no	—
178	C₄×C₄₇	—	2	8	no	—
179	C₄×C₄₇	C₂×#117	1	8	yes	—
180	Dic₄₇	—	2	8	no	—
181	Dic₄₇	—	4	8	no	—
182	Dic₄₇	—	4	4	no	—
183	C₂²×#117	D₄₇	1	1	yes	characteristic
184	#2347	—	47	16	no	—
185	C₂×#389	—	47	2	no	—
186	C₂×#388	—	47	4	no	—
187	C₂×#383	—	47	2	no	—
188	C₂×#380	—	47	1	no	—
189	C₂×C₄×C₄⋊C₄	—	47	2	no	—
190	C₂×C₄×C₄⋊C₄	—	47	2	no	—
191	C₂×C₄×C₂²⋊C₄	—	47	1	no	—
192	C₂×C₄₇	—	4	4	no	—
193	C₂×C₄₇	#2347	1	8	yes	complemented
194	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
195	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
196	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
197	C₂×C₄₇	C₂×#553	1	2	yes	—
198	C₂×C₄₇	C₂×#556	1	2	yes	—
199	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
200	C₂×#117	Dic₄₇	1	16	yes	complemented
201	C₂×#117	C₂×D₄₇	1	8	yes	—
202	C₂²×C₄⋊C₄	—	47	2	no	—
203	C₂²×C₄⋊C₄	—	47	4	no	—
204	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	—	47	2	no	—
207	C₂²×C₂²⋊C₄	—	47	2	no	—
208	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
209	C₂²×C₄²	—	47	2	no	—
210	C₂²×C₄²	—	47	4	no	—
211	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
212	#389	—	47	16	no	—
213	#388	—	47	32	no	—
214	#383	—	47	16	no	—
215	#380	—	47	8	no	—
216	C₄×C₄⋊C₄	—	47	16	no	—
217	C₄×C₄⋊C₄	—	47	16	no	—
218	C₄×C₂²⋊C₄	—	47	8	no	—
219	C₂×#95	—	47	1	no	—
220	C₂×#95	—	47	1	no	—
221	C₂×#95	—	47	2	no	—
222	C₂×#95	—	47	4	no	—
223	C₂×#95	—	47	4	no	—
224	C₄₇	C₂×#2347	1	1	yes	characteristic, complemented, Sylow
225	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
226	C₂³×C₄	—	2	8	no	—
227	C₂³×C₄	—	47	2	no	—
228	C₂³×C₄	—	47	4	no	—
229	C₂³×C₄	—	47	2	no	—
230	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
231	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
232	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
233	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
234	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	#117	C₂×Dic₄₇	1	64	yes	complemented
237	C₂×C₄⋊C₄	—	47	8	no	—
238	C₂×C₄⋊C₄	—	47	16	no	—
239	C₂×C₄⋊C₄	—	94	16	no	—
240	C₂×C₄⋊C₄	—	94	8	no	—
241	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
242	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
243	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
244	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
245	C₂×C₂²⋊C₄	—	47	8	no	—
246	C₂×C₂²⋊C₄	—	47	8	no	—
247	C₂×C₂²⋊C₄	—	94	8	no	—
248	C₂×C₂²⋊C₄	—	188	4	no	—
249	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	—
250	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
251	C₂×C₄²	—	47	8	no	—
252	C₂×C₄²	—	47	16	no	—
253	C₂×C₄²	—	94	8	no	—
254	C₂×C₄²	—	188	8	no	—
255	C₂×C₄²	C₂×Dic₄₇	1	16	yes	—
256	C₂×C₄²	C₂²×D₄₇	1	8	yes	—
257	#95	—	47	4	no	—
258	#95	—	47	4	no	—
259	#95	—	47	8	no	—
260	#95	—	47	16	no	—
261	#95	—	47	16	no	—
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	2	no	—
265	C₂⁴	—	2	2	no	—
266	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
267	C₂⁴	C₂³×D₄₇	1	2	yes	—
268	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	32	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	47	8	no	—
276	C₂²×C₄	—	47	4	no	—
277	C₂²×C₄	—	47	4	no	—
278	C₂²×C₄	—	47	8	no	—
279	C₂²×C₄	—	94	4	no	—
280	C₂²×C₄	—	94	4	no	—
281	C₂²×C₄	—	94	4	no	—
282	C₂²×C₄	—	94	8	no	—
283	C₂²×C₄	—	94	4	no	—
284	C₂²×C₄	—	94	8	no	—
285	C₂²×C₄	—	94	8	no	—
286	C₂²×C₄	—	94	4	no	—
287	C₂²×C₄	#10625350	1	8	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
293	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
294	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
295	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
296	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
297	C₄⋊C₄	—	94	32	no	—
298	C₄⋊C₄	—	94	16	no	—
299	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
300	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	—
301	C₂²⋊C₄	—	94	16	no	—
302	C₂²⋊C₄	—	188	8	no	—
303	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	—
304	C₄²	—	94	16	no	—
305	C₄²	—	188	16	no	—
306	C₄²	C₂²×Dic₄₇	1	32	yes	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	4	8	no	—
316	C₂³	C₂³×Dic₄₇	1	4	yes	—
317	C₂³	C₂³×Dic₄₇	1	2	yes	—
318	C₂³	#41×D₄₇	1	4	yes	—
319	C₂³	C₂×#10625350	1	4	yes	—
320	C₂³	#13094070	1	2	yes	—
321	C₂³	#13094071	1	2	yes	—
322	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	32	no	—
331	C₂×C₄	—	47	8	no	—
332	C₂×C₄	—	94	16	no	—
333	C₂×C₄	—	94	4	no	—
334	C₂×C₄	—	94	4	no	—
335	C₂×C₄	—	94	4	no	—
336	C₂×C₄	—	94	8	no	—
337	C₂×C₄	—	94	4	no	—
338	C₂×C₄	—	94	8	no	—
339	C₂×C₄	—	94	8	no	—
340	C₂×C₄	—	94	4	no	—
341	C₂×C₄	—	188	16	no	—
342	C₂×C₄	—	188	8	no	—
343	C₂×C₄	#13093983	1	16	yes	—
344	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
345	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
346	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
347	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
348	C₂×C₄	C₂×#10625350	1	8	yes	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	4	16	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	C₂×#13093983	1	4	yes	—
356	C₂²	#41×Dic₄₇	1	4	yes	—
357	C₂²	#15689606	1	4	yes	—
358	C₂²	#15689817	1	8	yes	—
359	C₂²	#15689841	1	8	yes	—
360	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
361	C₂²	C₂×#41×D₄₇	1	2	yes	—
362	C₂²	C₂²×#10625350	1	2	yes	—
363	C₂²	C₂×#13094070	1	1	yes	characteristic
364	C₂²	C₂×#13094071	1	1	yes	characteristic
365	C₄	—	2	4	no	—
366	C₄	—	2	8	no	—
367	C₄	—	2	8	no	—
368	C₄	—	94	8	no	—
369	C₄	—	188	8	no	—
370	C₄	—	188	4	no	—
371	C₄	C₂×#13093983	1	8	yes	—
372	C₂	—	4	4	no	—
373	C₂	#20246281	1	8	yes	direct product factor
374	C₂	C₂²×#13093983	1	1	yes	characteristic
375	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
376	C₂	C₂×#15689606	1	1	yes	characteristic
377	C₂	C₂×#15689817	1	2	yes	—
378	C₂	C₂×#15689841	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂×#2347
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #20246281	C₂	direct (N × H)
2. C₂×#15689022	C₂	semidirect
4. C₂×#15688991	C₂	semidirect
6. C₂×C₄⋊C₄×Dic₄₇	C₂	semidirect
7. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
16. #15689022	C₂²	semidirect
18. #15688991	C₂²	semidirect
20. C₄⋊C₄×Dic₄₇	C₂²	semidirect
21. C₄×C₄⋊Dic₄₇	C₂²	semidirect
29. C₂×#117×C₄₇	C₄	semidirect
63. #117×C₄₇	C₂×C₄	semidirect
193. C₂×C₄₇	#2347	semidirect
200. C₂×#117	Dic₄₇	semidirect
224. C₄₇	C₂×#2347	semidirect
236. #117	C₂×Dic₄₇	semidirect
373. C₂	#20246281	direct (N × H)

Maximal subgroups

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

subgroup	index
#20246281	2
C₂×#15689022	2
C₂×#15689016	2
C₂×#15688991	2
C₂×#15688983	2
C₂×C₄⋊C₄×Dic₄₇	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂²×#117×C₄₇	2
C₂×#2347	47

Subgroups — C2×#20246281 #26375541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246281 #26375541