Subgroups — C₂×#20243081 #26213632

Order 12032.

2782 conjugacy classes of subgroups.

The subgroup lattice has 372 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	C₂³×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243081	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688877	C₂	1	4	yes	maximal, complemented
5	C₂³×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×Dic₄₇	C₄	1	2	yes	—
7	C₂²×#10625329	—	2	4	no	—
8	C₂²×#10625329	—	2	4	no	—
9	C₂²×#10625329	C₄	1	8	yes	complemented
10	C₂²×#10625329	C₂²	1	4	yes	—
11	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
12	C₂²×C₄×Dic₄₇	—	2	4	no	—
13	C₂²×C₄×Dic₄₇	—	2	4	no	—
14	C₂²×C₄×Dic₄₇	C₄	1	4	yes	—
15	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
16	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
17	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
18	#15688877	C₂²	1	16	yes	complemented
19	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₇	—	2	4	no	—
21	C₂²×M₁₆×C₄₇	—	2	4	no	—
22	C₂²×M₁₆×C₄₇	C₄	1	8	yes	complemented
23	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
24	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
25	C₂³×Dic₄₇	—	2	8	no	—
26	C₂³×Dic₄₇	—	2	16	no	—
27	C₂³×Dic₄₇	C₂×C₄	1	8	yes	—
28	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
29	C₂×#10625329	—	2	32	no	—
30	C₂×#10625329	—	2	8	no	—
31	C₂×#10625329	—	2	8	no	—
32	C₂×#10625329	C₂×C₄	1	16	yes	complemented
33	C₂²×C₄₇⋊C₈	—	2	4	no	—
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
36	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
37	C₂×C₄×Dic₄₇	—	2	16	no	—
38	C₂×C₄×Dic₄₇	—	2	8	no	—
39	C₂×C₄×Dic₄₇	—	2	4	no	—
40	C₂×C₄×Dic₄₇	—	2	8	no	—
41	C₂×C₄×Dic₄₇	—	2	4	no	—
42	C₂×C₄×Dic₄₇	—	2	8	no	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
45	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
46	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₇	D₄	1	4	yes	—
52	C₂³×C₄×C₄₇	D₄	1	4	yes	—
53	C₂³×C₄×C₄₇	D₄	1	4	yes	—
54	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₄₇	—	2	32	no	—
58	C₂×M₁₆×C₄₇	—	2	8	no	—
59	C₂×M₁₆×C₄₇	—	2	8	no	—
60	C₂×M₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
61	C₂²×C₈×C₄₇	—	2	4	no	—
62	C₂²×C₈×C₄₇	—	2	4	no	—
63	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
64	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
65	C₂⁴×C₄₇	—	2	8	no	—
66	C₂⁴×C₄₇	C₄²	1	4	yes	—
67	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
68	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
69	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₄²	1	8	yes	—
72	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
77	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	—
78	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	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	4	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	64	no	—
97	C₂²×Dic₄₇	—	2	16	no	—
98	C₂²×Dic₄₇	—	2	8	no	—
99	C₂²×Dic₄₇	—	2	8	no	—
100	C₂²×Dic₄₇	—	2	32	no	—
101	C₂²×Dic₄₇	M₁₆	1	16	yes	complemented
102	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
103	M₁₆×C₄₇	—	2	32	no	—
104	C₂×C₈×C₄₇	—	2	16	no	—
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	2	4	no	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	complemented
108	C₄×Dic₄₇	—	2	8	no	—
109	C₄×Dic₄₇	—	2	16	no	—
110	C₄×Dic₄₇	—	2	4	no	—
111	C₄×Dic₄₇	—	2	4	no	—
112	#10625329	—	2	32	no	—
113	C₂×C₄₇⋊C₈	—	2	16	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	complemented
117	C₂³×C₄₇	—	2	8	no	—
118	C₂³×C₄₇	—	2	16	no	—
119	C₂³×C₄₇	—	2	16	no	—
120	C₂³×C₄₇	—	2	16	no	—
121	C₂³×C₄₇	#95	1	16	yes	—
122	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
123	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
126	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
127	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₄₇	C₂×M₁₆	1	8	yes	—
129	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#95	1	32	yes	—
131	C₂×C₄×C₄₇	#95	1	16	yes	—
132	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
134	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
136	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
139	C₂×C₄×C₄₇	C₂×C₂²⋊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	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂³×C₄	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×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	C₂×Dic₄₇	—	2	64	no	—
153	C₂×Dic₄₇	—	2	8	no	—
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	2	32	no	—
156	C₂×Dic₄₇	C₂×M₁₆	1	16	yes	complemented
157	C₈×C₄₇	—	2	8	no	—
158	C₄₇⋊C₈	—	2	8	no	—
159	C₂×#1728	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	8	no	—
162	C₂²×C₄₇	—	2	8	no	—
163	C₂²×C₄₇	—	2	32	no	—
164	C₂²×C₄₇	C₂×#95	1	8	yes	—
165	C₂²×C₄₇	C₂×#95	1	4	yes	—
166	C₂²×C₄₇	C₄×M₁₆	1	8	yes	—
167	C₂²×C₄₇	#407	1	8	yes	—
168	C₂²×C₄₇	#423	1	8	yes	—
169	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×C₄₇	C₂²×M₁₆	1	4	yes	—
173	C₄×C₄₇	C₂×#95	1	4	yes	—
174	C₄×C₄₇	C₂×#95	1	8	yes	—
175	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
179	Dic₄₇	—	2	16	no	—
180	C₂³×M₁₆	—	47	1	no	—
181	C₂³×M₁₆	D₄₇	1	1	yes	characteristic
182	C₂³×C₄²	—	47	1	no	—
183	#1728	—	47	8	no	—
184	C₂×#336	—	47	4	no	—
185	C₂×C₄₇	—	2	8	no	—
186	C₂×C₄₇	#1728	1	8	yes	complemented
187	C₂×C₄₇	C₂²×#95	1	1	yes	characteristic
188	C₂×C₄₇	C₂×C₄×M₁₆	1	2	yes	—
189	C₂×C₄₇	C₂×#407	1	2	yes	—
190	C₂×C₄₇	C₂×#423	1	2	yes	—
191	C₂⁴×C₄	—	47	2	no	—
192	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
193	C₂²×M₁₆	—	2	4	no	—
194	C₂²×M₁₆	—	2	4	no	—
195	C₂²×M₁₆	—	47	8	no	—
196	C₂²×M₁₆	—	47	4	no	—
197	C₂²×M₁₆	—	94	4	no	—
198	C₂²×M₁₆	—	94	4	no	—
199	C₂²×M₁₆	Dic₄₇	1	8	yes	complemented
200	C₂²×M₁₆	C₂×D₄₇	1	4	yes	—
201	C₂³×C₈	—	47	2	no	—
202	C₂³×C₈	C₂×D₄₇	1	2	yes	—
203	C₂²×C₄²	—	47	2	no	—
204	C₂²×C₄²	—	47	4	no	—
205	C₂²×C₄²	—	47	4	no	—
206	C₂²×C₄²	—	47	2	no	—
207	C₂²×C₄²	—	94	4	no	—
208	C₂²×C₄²	—	94	4	no	—
209	#336	—	47	16	no	—
210	C₄₇	C₂×#1728	1	1	yes	characteristic, complemented, Sylow
211	C₂⁵	C₄×D₄₇	1	1	yes	characteristic
212	C₂³×C₄	—	47	4	no	—
213	C₂³×C₄	—	47	8	no	—
214	C₂³×C₄	—	94	16	no	—
215	C₂³×C₄	—	94	8	no	—
216	C₂³×C₄	Dic₉₄	1	4	yes	—
217	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₄×D₄₇	1	2	yes	—
219	C₂³×C₄	C₄×D₄₇	1	4	yes	—
220	C₂³×C₄	D₁₈₈	1	4	yes	—
221	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
222	C₂³×C₄	C₂²⋊D₄₇	1	4	yes	—
223	C₂³×C₄	C₂²⋊D₄₇	1	4	yes	—
224	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
225	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
226	C₂×M₁₆	—	2	32	no	—
227	C₂×M₁₆	—	2	8	no	—
228	C₂×M₁₆	—	2	8	no	—
229	C₂×M₁₆	—	47	16	no	—
230	C₂×M₁₆	—	94	32	no	—
231	C₂×M₁₆	—	94	8	no	—
232	C₂×M₁₆	—	94	8	no	—
233	C₂×M₁₆	C₂×Dic₄₇	1	16	yes	complemented
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	47	8	no	—
237	C₂²×C₈	—	47	4	no	—
238	C₂²×C₈	—	94	4	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
241	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
242	C₂×C₄²	—	47	8	no	—
243	C₂×C₄²	—	47	4	no	—
244	C₂×C₄²	—	47	4	no	—
245	C₂×C₄²	—	94	16	no	—
246	C₂×C₄²	—	94	8	no	—
247	C₂×C₄²	—	94	4	no	—
248	C₂×C₄²	—	94	8	no	—
249	C₂×C₄²	—	94	4	no	—
250	C₂×C₄²	—	94	8	no	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	C₄×Dic₄₇	1	4	yes	—
253	C₂⁴	Dic₄₇⋊C₄	1	4	yes	—
254	C₂⁴	(C₂×D₄₇)⋊C₄	1	4	yes	—
255	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
256	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
257	C₂²×C₄	—	47	16	no	—
258	C₂²×C₄	—	47	8	no	—
259	C₂²×C₄	—	94	32	no	—
260	C₂²×C₄	—	94	64	no	—
261	C₂²×C₄	—	94	16	no	—
262	C₂²×C₄	—	94	8	no	—
263	C₂²×C₄	—	94	8	no	—
264	C₂²×C₄	C₄×Dic₄₇	1	8	yes	—
265	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
266	C₂²×C₄	Dic₄₇⋊C₄	1	8	yes	—
267	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
268	C₂²×C₄	Dic₄₇⋊C₄	1	16	yes	—
269	C₂²×C₄	C₄⋊Dic₄₇	1	16	yes	—
270	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	8	yes	—
271	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
272	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	16	yes	—
273	C₂²×C₄	C₂²⋊Dic₄₇	1	16	yes	—
274	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
275	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
276	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
277	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
279	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
280	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
281	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	M₁₆	—	2	32	no	—
290	M₁₆	—	94	32	no	—
291	C₂×C₈	—	2	16	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	47	8	no	—
295	C₂×C₈	—	94	16	no	—
296	C₂×C₈	—	94	4	no	—
297	C₂×C₈	—	94	4	no	—
298	C₂×C₈	C₂²×Dic₄₇	1	8	yes	complemented
299	C₄²	—	94	16	no	—
300	C₄²	—	94	8	no	—
301	C₄²	—	94	4	no	—
302	C₄²	—	94	4	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	C₄₇⋊#95	1	16	yes	—
308	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
309	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
310	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
311	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
312	C₂³	C₂×Dic₄₇⋊C₄	1	4	yes	—
313	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
314	C₂³	M₁₆×D₄₇	1	8	yes	—
315	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
316	C₂×C₄	—	47	16	no	—
317	C₂×C₄	—	94	64	no	—
318	C₂×C₄	—	94	8	no	—
319	C₂×C₄	—	94	32	no	—
320	C₂×C₄	—	94	8	no	—
321	C₂×C₄	C₄₇⋊#95	1	32	yes	—
322	C₂×C₄	C₄₇⋊#95	1	16	yes	—
323	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
324	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
325	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
326	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
327	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	4	yes	—
328	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	8	yes	—
329	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
330	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
331	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
332	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
333	C₂×C₄	C₂×Dic₄₇⋊C₄	1	8	yes	—
334	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
335	C₂×C₄	C₂×C₄⋊Dic₄₇	1	8	yes	—
336	C₂×C₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
342	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
343	C₈	—	2	8	no	—
344	C₈	—	94	8	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	2	32	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	8	no	—
349	C₂²	C₂×C₄₇⋊#95	1	8	yes	—
350	C₂²	C₂×C₄₇⋊#95	1	4	yes	—
351	C₂²	M₁₆×Dic₄₇	1	8	yes	—
352	C₂²	#15689086	1	8	yes	—
353	C₂²	#15689146	1	8	yes	—
354	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
355	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
356	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
357	C₂²	C₂×M₁₆×D₄₇	1	4	yes	—
358	C₄	—	94	16	no	—
359	C₄	C₂×C₄₇⋊#95	1	4	yes	—
360	C₄	C₂×C₄₇⋊#95	1	8	yes	—
361	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
362	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
363	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
364	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
365	C₂	—	2	8	no	—
366	C₂	#20243081	1	8	yes	direct product factor
367	C₂	C₂²×C₄₇⋊#95	1	1	yes	characteristic
368	C₂	C₂×M₁₆×Dic₄₇	1	2	yes	—
369	C₂	C₂×#15689086	1	2	yes	—
370	C₂	C₂×#15689146	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂³×M₁₆×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×M₁₆	D₄₇
hypocenter	C₄₇	C₂×#1728
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20243081	C₂	direct (N × H)
4. C₂×#15688877	C₂	semidirect
9. C₂²×#10625329	C₄	semidirect
18. #15688877	C₂²	semidirect
22. C₂²×M₁₆×C₄₇	C₄	semidirect
32. C₂×#10625329	C₂×C₄	semidirect
35. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
60. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
63. C₂²×C₈×C₄₇	C₂×C₄	semidirect
101. C₂²×Dic₄₇	M₁₆	semidirect
107. C₂×C₈×C₄₇	C₂²×C₄	semidirect
116. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
156. C₂×Dic₄₇	C₂×M₁₆	semidirect
186. C₂×C₄₇	#1728	semidirect
199. C₂²×M₁₆	Dic₄₇	semidirect
210. C₄₇	C₂×#1728	semidirect
233. C₂×M₁₆	C₂×Dic₄₇	semidirect
240. C₂²×C₈	C₂×Dic₄₇	semidirect
298. C₂×C₈	C₂²×Dic₄₇	semidirect
366. C₂	#20243081	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
C₂³×C₄×Dic₄₇	2
#20243081	2
C₂×#15688877	2
C₂³×M₁₆×C₄₇	2
C₂×#1728	47

Subgroups — C2×#20243081 #26213632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243081 #26213632