Subgroups — C₂×#20243085 #26213637

Order 12032.

2350 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20243085	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688878	C₂	1	4	yes	maximal, complemented
5	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	4	no	—
7	C₂²×#10625329	—	2	4	no	—
8	C₂²×#10625329	C₄	1	8	yes	complemented
9	C₂²×#10625329	C₂²	1	4	yes	—
10	C₂³×C₄₇⋊C₈	—	2	4	no	—
11	C₂³×C₄₇⋊C₈	—	2	4	no	—
12	C₂³×C₄₇⋊C₈	C₄	1	8	yes	complemented
13	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₄₇⋊C₈	C₂²	1	4	yes	—
16	#15688878	C₂²	1	16	yes	complemented
17	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₇	—	2	4	no	—
19	C₂×#117×C₄₇	—	2	4	no	—
20	C₂×#117×C₄₇	C₄	1	4	yes	—
21	C₂×#117×C₄₇	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
25	C₂×#10625329	—	2	32	no	—
26	C₂×#10625329	—	2	8	no	—
27	C₂×#10625329	—	2	8	no	—
28	C₂×#10625329	C₂×C₄	1	16	yes	complemented
29	C₂²×C₄₇⋊C₈	—	2	32	no	—
30	C₂²×C₄₇⋊C₈	—	2	4	no	—
31	C₂²×C₄₇⋊C₈	—	2	4	no	—
32	C₂²×C₄₇⋊C₈	—	2	8	no	—
33	C₂²×C₄₇⋊C₈	—	2	8	no	—
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	2	4	no	—
36	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
37	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
38	C₂²×C₄₇⋊C₈	C₂×C₄	1	16	yes	complemented
39	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂³×C₄×C₄₇	D₄	1	4	yes	—
48	C₂³×C₄×C₄₇	D₄	1	4	yes	—
49	C₂³×C₄×C₄₇	D₄	1	4	yes	—
50	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	#117×C₄₇	—	2	16	no	—
54	#117×C₄₇	—	2	8	no	—
55	#117×C₄₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
60	C₂×C₄²×C₄₇	—	2	4	no	—
61	C₂×C₄²×C₄₇	—	2	4	no	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
64	C₂⁴×C₄₇	—	2	8	no	—
65	C₂⁴×C₄₇	C₄²	1	4	yes	—
66	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
67	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
68	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	16	no	—
72	C₂²×C₄×C₄₇	C₄²	1	8	yes	—
73	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
78	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₄⋊C₄×C₄₇	—	2	16	no	—
99	C₂²⋊C₄×C₄₇	—	2	16	no	—
100	C₄²×C₄₇	—	2	8	no	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	4	no	—
103	#10625329	—	2	32	no	—
104	C₂×C₄₇⋊C₈	—	2	16	no	—
105	C₂×C₄₇⋊C₈	—	2	32	no	—
106	C₂×C₄₇⋊C₈	—	2	16	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
112	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
113	C₂³×C₄₇	—	2	8	no	—
114	C₂³×C₄₇	—	2	16	no	—
115	C₂³×C₄₇	—	2	16	no	—
116	C₂³×C₄₇	—	2	16	no	—
117	C₂³×C₄₇	#95	1	16	yes	—
118	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
119	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
121	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
122	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
123	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
124	C₂³×C₄₇	#131	1	8	yes	—
125	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	16	no	—
128	C₂×C₄×C₄₇	—	4	16	no	—
129	C₂×C₄×C₄₇	#95	1	32	yes	—
130	C₂×C₄×C₄₇	#95	1	16	yes	—
131	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
133	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
151	C₄₇⋊C₈	—	2	8	no	—
152	C₄₇⋊C₈	—	2	8	no	—
153	C₂×#1729	—	47	1	no	maximal, Sylow
154	C₂²×C₄₇	—	2	8	no	—
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	8	no	—
157	C₂²×C₄₇	—	2	32	no	—
158	C₂²×C₄₇	C₂×#95	1	8	yes	—
159	C₂²×C₄₇	C₂×#95	1	4	yes	—
160	C₂²×C₄₇	#405	1	8	yes	—
161	C₂²×C₄₇	#408	1	8	yes	—
162	C₂²×C₄₇	#424	1	8	yes	—
163	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
164	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×#131	1	4	yes	—
167	C₄×C₄₇	—	4	8	no	—
168	C₄×C₄₇	C₂×#95	1	4	yes	—
169	C₄×C₄₇	C₂×#95	1	8	yes	—
170	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂³×M₁₆	—	47	1	no	—
175	C₂⁴×C₈	—	47	1	no	—
176	C₂²×#117	D₄₇	1	1	yes	characteristic
177	#1729	—	47	8	no	—
178	C₂×#336	—	47	4	no	—
179	C₂×C₄₇	—	2	8	no	—
180	C₂×C₄₇	#1729	1	8	yes	complemented
181	C₂×C₄₇	C₂²×#95	1	1	yes	characteristic
182	C₂×C₄₇	C₂×#405	1	2	yes	—
183	C₂×C₄₇	C₂×#408	1	2	yes	—
184	C₂×C₄₇	C₂×#424	1	2	yes	—
185	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
186	C₂²×M₁₆	—	47	8	no	—
187	C₂²×M₁₆	—	47	4	no	—
188	C₂²×M₁₆	—	94	4	no	—
189	C₂²×M₁₆	—	94	4	no	—
190	C₂³×C₈	—	47	8	no	—
191	C₂³×C₈	—	47	4	no	—
192	C₂³×C₈	—	47	2	no	—
193	C₂³×C₈	—	47	2	no	—
194	C₂³×C₈	—	94	4	no	—
195	C₂³×C₈	—	94	4	no	—
196	C₂×#117	—	2	4	no	—
197	C₂×#117	—	2	4	no	—
198	C₂×#117	Dic₄₇	1	4	yes	—
199	C₂×#117	C₂×D₄₇	1	4	yes	—
200	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
201	C₂²×C₂²⋊C₄	Dic₄₇	1	2	yes	—
202	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
203	#336	—	47	16	no	—
204	C₄₇	C₂×#1729	1	1	yes	characteristic, complemented, Sylow
205	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
206	C₂³×C₄	Dic₉₄	1	4	yes	—
207	C₂³×C₄	C₄×D₄₇	1	4	yes	—
208	C₂³×C₄	C₄×D₄₇	1	4	yes	—
209	C₂³×C₄	D₁₈₈	1	4	yes	—
210	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
211	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
212	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
213	C₂³×C₄	C₂²⋊D₄₇	1	4	yes	—
214	C₂³×C₄	C₂²⋊D₄₇	1	4	yes	—
215	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
216	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
217	C₂×M₁₆	—	47	16	no	—
218	C₂×M₁₆	—	94	32	no	—
219	C₂×M₁₆	—	94	8	no	—
220	C₂×M₁₆	—	94	8	no	—
221	C₂²×C₈	—	47	8	no	—
222	C₂²×C₈	—	47	16	no	—
223	C₂²×C₈	—	47	8	no	—
224	C₂²×C₈	—	47	4	no	—
225	C₂²×C₈	—	47	4	no	—
226	C₂²×C₈	—	94	32	no	—
227	C₂²×C₈	—	94	4	no	—
228	C₂²×C₈	—	94	8	no	—
229	C₂²×C₈	—	94	4	no	—
230	C₂²×C₈	—	94	4	no	—
231	C₂²×C₈	—	94	8	no	—
232	C₂²×C₈	—	94	4	no	—
233	#117	—	2	16	no	—
234	#117	—	2	8	no	—
235	#117	—	2	8	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
238	C₂×C₂²⋊C₄	—	2	8	no	—
239	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	8	yes	—
240	C₂×C₄²	—	2	4	no	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
243	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	C₄×Dic₄₇	1	4	yes	—
246	C₂⁴	C₄⋊Dic₄₇	1	4	yes	—
247	C₂⁴	C₂²⋊Dic₄₇	1	4	yes	—
248	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
249	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	8	no	—
251	C₂²×C₄	—	2	16	no	—
252	C₂²×C₄	C₄×Dic₄₇	1	8	yes	—
253	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
254	C₂²×C₄	Dic₄₇⋊C₄	1	16	yes	—
255	C₂²×C₄	Dic₄₇⋊C₄	1	16	yes	—
256	C₂²×C₄	C₄⋊Dic₄₇	1	8	yes	—
257	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
258	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	16	yes	—
259	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	16	yes	—
260	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
261	C₂²×C₄	C₂²⋊Dic₄₇	1	8	yes	—
262	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
263	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
264	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
265	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
266	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
268	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
269	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
270	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
271	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
273	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
274	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
277	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
278	M₁₆	—	94	32	no	—
279	C₂×C₈	—	47	8	no	—
280	C₂×C₈	—	47	8	no	—
281	C₂×C₈	—	94	16	no	—
282	C₂×C₈	—	94	32	no	—
283	C₂×C₈	—	94	16	no	—
284	C₂×C₈	—	94	4	no	—
285	C₂×C₈	—	94	4	no	—
286	C₂×C₈	—	94	4	no	—
287	C₂×C₈	—	94	4	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₂²⋊C₄	—	2	16	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	2	16	no	—
295	C₂³	—	2	8	no	—
296	C₂³	—	2	16	no	—
297	C₂³	C₄₇⋊#95	1	16	yes	—
298	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
299	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
300	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
301	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
302	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
303	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
304	C₂³	#13094031	1	8	yes	—
305	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	16	no	—
308	C₂×C₄	—	4	16	no	—
309	C₂×C₄	C₄₇⋊#95	1	32	yes	—
310	C₂×C₄	C₄₇⋊#95	1	16	yes	—
311	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
312	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
313	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	8	yes	—
314	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
315	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
316	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	8	yes	—
317	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
318	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
319	C₂×C₄	C₂×Dic₄₇⋊C₄	1	8	yes	—
320	C₂×C₄	C₂×Dic₄₇⋊C₄	1	8	yes	—
321	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
322	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
323	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
324	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
325	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
326	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
330	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
331	C₈	—	94	8	no	—
332	C₈	—	94	8	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	32	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	8	no	—
337	C₂²	C₂×C₄₇⋊#95	1	8	yes	—
338	C₂²	C₂×C₄₇⋊#95	1	4	yes	—
339	C₂²	#15689079	1	8	yes	—
340	C₂²	#15689090	1	8	yes	—
341	C₂²	#15689150	1	8	yes	—
342	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
343	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
345	C₂²	C₂×#13094031	1	4	yes	—
346	C₄	—	4	8	no	—
347	C₄	C₂×C₄₇⋊#95	1	4	yes	—
348	C₄	C₂×C₄₇⋊#95	1	8	yes	—
349	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
350	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
351	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
352	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
353	C₂	—	2	8	no	—
354	C₂	#20243085	1	8	yes	direct product factor
355	C₂	C₂²×C₄₇⋊#95	1	1	yes	characteristic
356	C₂	C₂×#15689079	1	2	yes	—
357	C₂	C₂×#15689090	1	2	yes	—
358	C₂	C₂×#15689150	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂×#1729
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
3. #20243085	C₂	direct (N × H)
4. C₂×#15688878	C₂	semidirect
8. C₂²×#10625329	C₄	semidirect
12. C₂³×C₄₇⋊C₈	C₄	semidirect
16. #15688878	C₂²	semidirect
28. C₂×#10625329	C₂×C₄	semidirect
38. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
180. C₂×C₄₇	#1729	semidirect
204. C₄₇	C₂×#1729	semidirect
354. C₂	#20243085	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625329	2
C₂⁴×C₄₇⋊C₈	2
#20243085	2
C₂×#15688878	2
C₂²×#117×C₄₇	2
C₂×#1729	47

Subgroups — C2×#20243085 #26213637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243085 #26213637