Subgroups — C₂×#20251833 #27079719

Order 12032.

5150 conjugacy classes of subgroups.

The subgroup lattice has 368 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	2	yes	maximal, complemented
2	#20251833	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689090	C₂	1	8	yes	maximal, complemented
4	C₂×#15689087	C₂	1	4	yes	maximal, complemented
5	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	—	2	16	no	—
7	C₂²×#10625329	C₂²	1	4	yes	—
8	C₂²×#10625329	C₂²	1	4	yes	complemented
9	C₂²×#10625329	C₂²	1	16	yes	complemented
10	C₂³×C₄₇⋊C₈	C₂²	1	4	yes	complemented
11	#15689090	C₂²	1	64	yes	complemented
12	#15689087	C₂²	1	32	yes	complemented
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
14	C₂²×#41×C₄₇	—	2	16	no	—
15	C₂²×#41×C₄₇	C₄	1	4	yes	—
16	C₂²×#41×C₄₇	C₄	1	8	yes	—
17	C₂²×#41×C₄₇	C₂²	1	4	yes	—
18	C₂²×#41×C₄₇	C₂²	1	8	yes	—
19	C₂³×Q₈×C₄₇	C₄	1	1	yes	characteristic
20	C₂³×D₄×C₄₇	C₄	1	2	yes	—
21	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic
22	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#10625329	—	2	16	no	—
25	C₂×#10625329	—	2	16	no	—
26	C₂×#10625329	—	2	64	no	—
27	C₂×#10625329	C₂³	1	16	yes	—
28	C₂×#10625329	C₂³	1	16	yes	complemented
29	C₂²×C₄₇⋊C₈	—	2	16	no	—
30	C₂²×C₄₇⋊C₈	C₂³	1	8	yes	—
31	C₂²×C₄₇⋊C₈	C₂³	1	16	yes	complemented
32	C₂²⋊(C₄₇⋊C₈)	C₂³	1	64	yes	complemented
33	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
34	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×#41×C₄₇	—	2	32	no	—
36	C₂×#41×C₄₇	—	2	64	no	—
37	C₂×#41×C₄₇	—	2	16	no	—
38	C₂×#41×C₄₇	—	2	16	no	—
39	C₂×#41×C₄₇	—	2	64	no	—
40	C₂×#41×C₄₇	C₂×C₄	1	16	yes	—
41	C₂×#41×C₄₇	C₂×C₄	1	32	yes	—
42	C₂×#41×C₄₇	C₂³	1	16	yes	—
43	C₂²×Q₈×C₄₇	—	2	8	no	—
44	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
46	C₂²×D₄×C₄₇	—	2	16	no	—
47	C₂²×D₄×C₄₇	—	2	8	no	—
48	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
49	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	—
50	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₂³×C₄×C₄₇	—	2	16	no	—
53	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
56	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂³×C₄×C₄₇	D₄	1	16	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
65	C₂⁴×C₄₇	—	2	8	no	—
66	C₂⁴×C₄₇	—	4	4	no	—
67	C₂⁴×C₄₇	—	4	8	no	—
68	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
69	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
73	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
74	#41×C₄₇	—	2	64	no	—
75	#41×C₄₇	—	2	128	no	—
76	#41×C₄₇	—	2	32	no	—
77	#41×C₄₇	—	2	32	no	—
78	C₂×Q₈×C₄₇	—	2	32	no	—
79	C₂×Q₈×C₄₇	—	2	16	no	—
80	C₂×Q₈×C₄₇	C₂²×C₄	1	16	yes	—
81	C₂×D₄×C₄₇	—	2	32	no	—
82	C₂×D₄×C₄₇	—	2	64	no	—
83	C₂×D₄×C₄₇	—	2	32	no	—
84	C₂×D₄×C₄₇	—	2	16	no	—
85	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	32	no	—
89	C₂²×C₄×C₄₇	—	2	16	no	—
90	C₂²×C₄×C₄₇	—	2	16	no	—
91	C₂²×C₄×C₄₇	—	2	32	no	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	32	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	32	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	#10625329	—	2	32	no	—
114	#10625329	—	2	32	no	—
115	C₂×C₄₇⋊C₈	—	2	16	no	—
116	C₂×C₄₇⋊C₈	—	2	32	no	—
117	C₂×C₄₇⋊C₈	C₂⁴	1	16	yes	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	8	no	—
120	C₂³×C₄₇	—	2	16	no	—
121	C₂³×C₄₇	—	2	8	no	—
122	C₂³×C₄₇	—	2	16	no	—
123	C₂³×C₄₇	—	4	16	no	—
124	C₂³×C₄₇	—	4	8	no	—
125	C₂³×C₄₇	—	4	16	no	—
126	C₂³×C₄₇	—	4	32	no	—
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
130	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
131	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
132	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
133	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
134	Q₈×C₄₇	—	2	32	no	—
135	D₄×C₄₇	—	2	64	no	—
136	D₄×C₄₇	—	2	32	no	—
137	C₂×C₄×C₄₇	—	2	16	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	2	16	no	—
140	C₂×C₄×C₄₇	—	2	32	no	—
141	C₂×C₄×C₄₇	—	2	16	no	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	32	yes	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
152	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
154	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
155	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
156	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
157	C₄₇⋊C₈	—	2	16	no	—
158	C₂×#2879	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	8	no	—
160	C₂²×C₄₇	—	2	16	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	8	no	—
163	C₂²×C₄₇	—	2	8	no	—
164	C₂²×C₄₇	—	2	16	no	—
165	C₂²×C₄₇	—	4	16	no	—
166	C₂²×C₄₇	—	4	32	no	—
167	C₂²×C₄₇	—	4	16	no	—
168	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
169	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄₇	#568	1	4	yes	—
172	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
173	C₄×C₄₇	—	2	8	no	—
174	C₄×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
175	C₄×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
176	C₄×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
177	C₄×C₄₇	C₂³×D₄	1	2	yes	—
178	C₂³×#41	D₄₇	1	1	yes	characteristic
179	C₂³×M₁₆	—	47	2	no	—
180	#2879	—	47	16	no	—
181	C₂×#408	—	47	8	no	—
182	C₂×#407	—	47	4	no	—
183	C₂×C₄₇	—	2	4	no	—
184	C₂×C₄₇	—	2	8	no	—
185	C₂×C₄₇	—	4	8	no	—
186	C₂×C₄₇	#2879	1	4	yes	complemented
187	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄₇	C₂×#568	1	2	yes	—
189	C₂²×#41	—	2	16	no	—
190	C₂²×#41	Dic₄₇	1	4	yes	—
191	C₂²×#41	Dic₄₇	1	8	yes	—
192	C₂²×#41	C₂×D₄₇	1	4	yes	—
193	C₂²×#41	C₂×D₄₇	1	8	yes	—
194	C₂³×Q₈	Dic₄₇	1	1	yes	characteristic
195	C₂³×D₄	Dic₄₇	1	2	yes	—
196	C₂³×D₄	Dic₄₇	1	1	yes	characteristic
197	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
198	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
199	C₂²×M₁₆	—	47	4	no	—
200	C₂²×M₁₆	—	47	4	no	—
201	C₂²×M₁₆	—	47	16	no	—
202	C₂²×M₁₆	—	94	16	no	—
203	C₂³×C₈	—	47	4	no	—
204	#408	—	47	64	no	—
205	#407	—	47	32	no	—
206	C₂×C₂²⋊C₈	—	47	16	no	—
207	C₄₇	C₂×#2879	1	1	yes	characteristic, complemented, Sylow
208	C₂⁵	C₂×Dic₄₇	1	2	yes	—
209	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
210	C₂×#41	—	2	32	no	—
211	C₂×#41	—	2	64	no	—
212	C₂×#41	—	2	16	no	—
213	C₂×#41	—	2	16	no	—
214	C₂×#41	—	2	64	no	—
215	C₂×#41	C₂×Dic₄₇	1	16	yes	—
216	C₂×#41	C₂×Dic₄₇	1	32	yes	—
217	C₂×#41	C₂²×D₄₇	1	16	yes	—
218	C₂²×Q₈	—	2	8	no	—
219	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
220	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	—
221	C₂²×D₄	—	2	16	no	—
222	C₂²×D₄	—	2	8	no	—
223	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
224	C₂²×D₄	C₂×Dic₄₇	1	16	yes	—
225	C₂²×D₄	C₂×Dic₄₇	1	4	yes	—
226	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
227	C₂³×C₄	—	2	16	no	—
228	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
229	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
230	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
231	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
233	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
234	C₂³×C₄	C₂²⋊D₄₇	1	16	yes	—
235	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
236	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
237	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₂×M₁₆	—	47	16	no	—
241	C₂×M₁₆	—	47	16	no	—
242	C₂×M₁₆	—	94	16	no	—
243	C₂×M₁₆	—	94	16	no	—
244	C₂×M₁₆	—	94	64	no	—
245	C₂²×C₈	—	47	16	no	—
246	C₂²×C₈	—	47	8	no	—
247	C₂²×C₈	—	94	16	no	—
248	C₂²⋊C₈	—	47	64	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	4	4	no	—
251	C₂⁴	—	4	8	no	—
252	C₂⁴	C₂²⋊Dic₄₇	1	8	yes	—
253	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
254	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
255	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
256	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
257	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
258	#41	—	2	64	no	—
259	#41	—	2	128	no	—
260	#41	—	2	32	no	—
261	#41	—	2	32	no	—
262	C₂×Q₈	—	2	32	no	—
263	C₂×Q₈	—	2	16	no	—
264	C₂×Q₈	C₂²×Dic₄₇	1	16	yes	—
265	C₂×D₄	—	2	32	no	—
266	C₂×D₄	—	2	64	no	—
267	C₂×D₄	—	2	32	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	C₂²×Dic₄₇	1	32	yes	—
270	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	32	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	32	no	—
276	C₂²×C₄	C₂²⋊Dic₄₇	1	8	yes	—
277	C₂²×C₄	C₂²⋊Dic₄₇	1	16	yes	—
278	C₂²×C₄	C₂²⋊Dic₄₇	1	32	yes	—
279	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
290	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
292	C₂²×C₄	C₂×C₂²⋊D₄₇	1	32	yes	—
293	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
294	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
295	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
296	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
297	M₁₆	—	94	32	no	—
298	M₁₆	—	94	32	no	—
299	C₂×C₈	—	47	16	no	—
300	C₂×C₈	—	94	16	no	—
301	C₂×C₈	—	94	32	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	4	16	no	—
308	C₂³	—	4	8	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	32	no	—
311	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
312	C₂³	C₂×C₂²⋊Dic₄₇	1	8	yes	—
313	C₂³	C₂×C₂²⋊Dic₄₇	1	16	yes	—
314	C₂³	C₂³×Dic₄₇	1	8	yes	—
315	C₂³	C₂³×Dic₄₇	1	2	yes	—
316	C₂³	C₂³×Dic₄₇	1	4	yes	—
317	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
318	Q₈	—	2	32	no	—
319	D₄	—	2	64	no	—
320	D₄	—	2	32	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	32	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
327	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
328	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	16	yes	—
329	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
330	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	16	yes	—
331	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	32	yes	—
332	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
333	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
334	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
335	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
336	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
337	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
338	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
339	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
340	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
341	C₈	—	94	16	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	16	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	16	no	—
348	C₂²	—	4	16	no	—
349	C₂²	—	4	32	no	—
350	C₂²	—	4	16	no	—
351	C₂²	C₂²×C₂²⋊Dic₄₇	1	4	yes	—
352	C₂²	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
353	C₂²	C₂²×C₂²⋊Dic₄₇	1	2	yes	—
354	C₂²	#15689890	1	4	yes	—
355	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
356	C₄	—	2	8	no	—
357	C₄	C₂²×C₂²⋊Dic₄₇	1	4	yes	—
358	C₄	C₂²×C₂²⋊Dic₄₇	1	2	yes	—
359	C₄	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
360	C₄	C₂³×C₂²⋊D₄₇	1	2	yes	—
361	C₂	—	2	4	no	—
362	C₂	—	2	8	no	—
363	C₂	—	4	8	no	—
364	C₂	#20251833	1	4	yes	direct product factor
365	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
366	C₂	C₂×#15689890	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂³×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×#41	D₄₇
hypocenter	C₄₇	C₂×#2879
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625329	C₂	semidirect
2. #20251833	C₂	direct (N × H)
3. C₂×#15689090	C₂	semidirect
4. C₂×#15689087	C₂	semidirect
8. C₂²×#10625329	C₂²	semidirect
9. C₂²×#10625329	C₂²	semidirect
10. C₂³×C₄₇⋊C₈	C₂²	semidirect
11. #15689090	C₂²	semidirect
12. #15689087	C₂²	semidirect
13. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
28. C₂×#10625329	C₂³	semidirect
31. C₂²×C₄₇⋊C₈	C₂³	semidirect
32. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
186. C₂×C₄₇	#2879	semidirect
207. C₄₇	C₂×#2879	semidirect
364. C₂	#20251833	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
#20251833	2
C₂×#15689090	2
C₂×#15689087	2
C₂³×#41×C₄₇	2
C₂×#2879	47

Subgroups — C2×#20251833 #27079719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20251833 #27079719