Group #26048005 — subgroups

Subgroups — C₄₇×#8307 #26048005

Order 12032.

1518 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1779	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#323	C₂	1	4	yes	maximal, complemented
4	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic
5	C₂³×D₄×C₄₇	C₄	1	2	yes	—
6	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×#121×C₄₇	—	2	4	no	—
8	C₂×#121×C₄₇	—	2	8	no	—
9	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
11	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
12	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
13	C₄₇×#323	—	2	8	no	—
14	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
16	C₂²×D₄×C₄₇	—	2	4	no	—
17	C₂²×D₄×C₄₇	—	2	4	no	—
18	C₂²×D₄×C₄₇	—	2	4	no	—
19	C₂²×D₄×C₄₇	—	2	2	no	—
20	C₂²×D₄×C₄₇	—	2	4	no	—
21	C₂²×D₄×C₄₇	—	4	4	no	—
22	C₂²×D₄×C₄₇	—	4	8	no	—
23	C₂³×C₄×C₄₇	—	2	4	no	—
24	C₂³×C₄×C₄₇	—	4	4	no	—
25	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₄₇	D₄	1	4	yes	—
28	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₄₇	—	2	4	no	—
30	#121×C₄₇	—	2	32	no	—
31	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
32	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
33	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
34	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
35	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	—
36	C₂²⋊C₈×C₄₇	—	2	8	no	—
37	C₂²⋊C₈×C₄₇	—	4	8	no	—
38	C₂⁴×C₄₇	—	2	4	no	—
39	C₂⁴×C₄₇	—	2	2	no	—
40	C₂⁴×C₄₇	—	2	2	no	—
41	C₂⁴×C₄₇	—	2	2	no	—
42	C₂⁴×C₄₇	—	2	4	no	—
43	C₂⁴×C₄₇	—	2	8	no	—
44	C₂⁴×C₄₇	—	4	2	no	—
45	C₂⁴×C₄₇	—	4	4	no	—
46	C₂⁴×C₄₇	—	4	4	no	—
47	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
48	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
49	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂×D₄×C₄₇	—	2	8	no	—
51	C₂×D₄×C₄₇	—	2	16	no	—
52	C₂×D₄×C₄₇	—	4	16	no	—
53	C₂×D₄×C₄₇	—	4	4	no	—
54	C₂×D₄×C₄₇	—	4	16	no	—
55	C₂×D₄×C₄₇	—	4	8	no	—
56	C₂×D₄×C₄₇	—	4	16	no	—
57	C₂×D₄×C₄₇	—	4	8	no	—
58	C₂×D₄×C₄₇	—	4	4	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	4	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	8	no	—
64	C₂²×C₄×C₄₇	—	2	8	no	—
65	C₂²×C₄×C₄₇	—	4	4	no	—
66	C₂²×C₄×C₄₇	—	4	2	no	—
67	C₂²×C₄×C₄₇	—	4	16	no	—
68	C₂²×C₄×C₄₇	—	4	4	no	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
71	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
73	C₂×C₈×C₄₇	—	4	8	no	—
74	C₂×C₈×C₄₇	—	4	4	no	—
75	C₄⋊C₄×C₄₇	—	2	8	no	—
76	C₂²⋊C₄×C₄₇	—	2	16	no	—
77	C₂³×C₄₇	—	2	2	no	—
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	—	2	8	no	—
80	C₂³×C₄₇	—	2	2	no	—
81	C₂³×C₄₇	—	2	4	no	—
82	C₂³×C₄₇	—	2	4	no	—
83	C₂³×C₄₇	—	2	2	no	—
84	C₂³×C₄₇	—	2	4	no	—
85	C₂³×C₄₇	—	2	8	no	—
86	C₂³×C₄₇	—	4	16	no	—
87	C₂³×C₄₇	—	4	4	no	—
88	C₂³×C₄₇	—	4	4	no	—
89	C₂³×C₄₇	—	4	4	no	—
90	C₂³×C₄₇	—	4	4	no	—
91	C₂³×C₄₇	—	4	4	no	—
92	C₂³×C₄₇	—	4	4	no	—
93	C₂³×C₄₇	—	4	4	no	—
94	C₂³×C₄₇	—	4	4	no	—
95	C₂³×C₄₇	—	4	4	no	—
96	C₂³×C₄₇	—	4	4	no	—
97	C₂³×C₄₇	—	8	16	no	—
98	C₂³×C₄₇	#100	1	4	yes	—
99	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
100	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂³×C₄₇	#131	1	4	yes	—
102	D₄×C₄₇	—	4	16	no	—
103	D₄×C₄₇	—	4	32	no	—
104	C₂×C₄×C₄₇	—	2	8	no	—
105	C₂×C₄×C₄₇	—	2	2	no	—
106	C₂×C₄×C₄₇	—	2	4	no	—
107	C₂×C₄×C₄₇	—	2	2	no	—
108	C₂×C₄×C₄₇	—	2	4	no	—
109	C₂×C₄×C₄₇	—	4	4	no	—
110	C₂×C₄×C₄₇	—	4	16	no	—
111	C₂×C₄×C₄₇	—	4	4	no	—
112	C₂×C₄×C₄₇	—	4	4	no	—
113	C₂×C₄×C₄₇	—	4	4	no	—
114	C₂×C₄×C₄₇	#99	1	4	yes	—
115	C₂×C₄×C₄₇	#120	1	4	yes	—
116	C₈×C₄₇	—	8	4	no	—
117	#8307	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂²×C₄₇	—	2	8	no	—
119	C₂²×C₄₇	—	2	2	no	—
120	C₂²×C₄₇	—	2	2	no	—
121	C₂²×C₄₇	—	2	8	no	—
122	C₂²×C₄₇	—	2	4	no	—
123	C₂²×C₄₇	—	4	16	no	—
124	C₂²×C₄₇	—	4	4	no	—
125	C₂²×C₄₇	—	4	2	no	—
126	C₂²×C₄₇	—	4	2	no	—
127	C₂²×C₄₇	—	4	4	no	—
128	C₂²×C₄₇	—	4	4	no	—
129	C₂²×C₄₇	—	4	4	no	—
130	C₂²×C₄₇	—	8	8	no	—
131	C₂²×C₄₇	—	8	8	no	—
132	C₂²×C₄₇	—	8	8	no	—
133	C₂²×C₄₇	#379	1	1	yes	characteristic
134	C₂²×C₄₇	#408	1	4	yes	—
135	C₂²×C₄₇	#408	1	2	yes	—
136	C₂²×C₄₇	C₂×#99	1	2	yes	—
137	C₂²×C₄₇	C₂×#100	1	2	yes	—
138	C₄×C₄₇	—	2	4	no	—
139	C₄×C₄₇	—	2	4	no	—
140	C₄×C₄₇	—	4	4	no	—
141	C₂²×#121	C₂×C₄₇	1	1	yes	characteristic
142	#1779	C₂×C₄₇	1	2	yes	complemented
143	C₂×#323	C₂×C₄₇	1	4	yes	complemented
144	C₂×C₄₇	—	2	4	no	—
145	C₂×C₄₇	—	4	4	no	—
146	C₂×C₄₇	—	8	4	no	—
147	C₂×C₄₇	#1471	1	4	yes	—
148	C₂×C₄₇	#1780	1	1	yes	characteristic
149	C₂×C₄₇	#1781	1	1	yes	characteristic
150	C₂×C₄₇	#1783	1	1	yes	characteristic
151	C₂³×D₄	C₄×C₄₇	1	1	yes	characteristic
152	C₂³×D₄	C₄×C₄₇	1	2	yes	—
153	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
154	C₂×#121	—	2	4	no	—
155	C₂×#121	—	2	8	no	—
156	C₂²×C₄⋊C₄	C₄×C₄₇	1	1	yes	characteristic
157	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
158	C₂×C₂²⋊C₈	—	2	4	no	—
159	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
160	#323	—	2	8	no	—
161	C₄₇	#8307	1	1	yes	characteristic, direct product factor, Sylow
162	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
163	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
164	C₂²×D₄	—	2	4	no	—
165	C₂²×D₄	—	2	4	no	—
166	C₂²×D₄	—	2	4	no	—
167	C₂²×D₄	—	2	2	no	—
168	C₂²×D₄	—	2	4	no	—
169	C₂²×D₄	—	4	4	no	—
170	C₂²×D₄	—	4	8	no	—
171	C₂³×C₄	—	2	4	no	—
172	C₂³×C₄	—	4	4	no	—
173	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
174	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
175	C₂³×C₄	D₄×C₄₇	1	4	yes	—
176	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
177	C₂²×C₈	—	2	4	no	—
178	#121	—	2	32	no	—
179	C₂×C₄⋊C₄	—	2	4	no	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₂²⋊C₄	—	2	4	no	—
183	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	—
184	C₂²⋊C₈	—	2	8	no	—
185	C₂²⋊C₈	—	4	8	no	—
186	C₂⁴	—	2	2	no	—
187	C₂⁴	—	2	4	no	—
188	C₂⁴	—	2	2	no	—
189	C₂⁴	—	2	2	no	—
190	C₂⁴	—	2	4	no	—
191	C₂⁴	—	2	8	no	—
192	C₂⁴	—	4	2	no	—
193	C₂⁴	—	4	4	no	—
194	C₂⁴	—	4	4	no	—
195	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
196	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
197	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
198	C₂×D₄	—	2	8	no	—
199	C₂×D₄	—	2	16	no	—
200	C₂×D₄	—	4	16	no	—
201	C₂×D₄	—	4	4	no	—
202	C₂×D₄	—	4	16	no	—
203	C₂×D₄	—	4	8	no	—
204	C₂×D₄	—	4	16	no	—
205	C₂×D₄	—	4	8	no	—
206	C₂×D₄	—	4	4	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	2	no	—
210	C₂²×C₄	—	2	2	no	—
211	C₂²×C₄	—	2	8	no	—
212	C₂²×C₄	—	2	8	no	—
213	C₂²×C₄	—	4	4	no	—
214	C₂²×C₄	—	4	2	no	—
215	C₂²×C₄	—	4	16	no	—
216	C₂²×C₄	—	4	4	no	—
217	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
218	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
219	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
220	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
221	C₂×C₈	—	4	8	no	—
222	C₂×C₈	—	4	4	no	—
223	C₄⋊C₄	—	2	8	no	—
224	C₂²⋊C₄	—	2	16	no	—
225	C₂³	—	2	2	no	—
226	C₂³	—	2	2	no	—
227	C₂³	—	2	8	no	—
228	C₂³	—	2	2	no	—
229	C₂³	—	2	4	no	—
230	C₂³	—	2	4	no	—
231	C₂³	—	2	2	no	—
232	C₂³	—	2	4	no	—
233	C₂³	—	2	8	no	—
234	C₂³	—	4	16	no	—
235	C₂³	—	4	4	no	—
236	C₂³	—	4	4	no	—
237	C₂³	—	4	4	no	—
238	C₂³	—	4	4	no	—
239	C₂³	—	4	4	no	—
240	C₂³	—	4	4	no	—
241	C₂³	—	4	4	no	—
242	C₂³	—	4	4	no	—
243	C₂³	—	4	4	no	—
244	C₂³	—	4	4	no	—
245	C₂³	—	8	16	no	—
246	C₂³	#100×C₄₇	1	4	yes	—
247	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
248	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
249	C₂³	#131×C₄₇	1	4	yes	—
250	D₄	—	4	16	no	—
251	D₄	—	4	32	no	—
252	C₂×C₄	—	2	8	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	4	4	no	—
258	C₂×C₄	—	4	16	no	—
259	C₂×C₄	—	4	4	no	—
260	C₂×C₄	—	4	4	no	—
261	C₂×C₄	—	4	4	no	—
262	C₂×C₄	#99×C₄₇	1	4	yes	—
263	C₂×C₄	#120×C₄₇	1	4	yes	—
264	C₈	—	8	4	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	2	8	no	—
268	C₂²	—	2	4	no	—
269	C₂²	—	2	8	no	—
270	C₂²	—	4	16	no	—
271	C₂²	—	4	2	no	—
272	C₂²	—	4	2	no	—
273	C₂²	—	4	4	no	—
274	C₂²	—	4	4	no	—
275	C₂²	—	4	4	no	—
276	C₂²	—	4	4	no	—
277	C₂²	—	8	8	no	—
278	C₂²	—	8	8	no	—
279	C₂²	—	8	8	no	—
280	C₂²	C₄₇×#379	1	1	yes	characteristic
281	C₂²	C₄₇×#408	1	4	yes	—
282	C₂²	C₄₇×#408	1	2	yes	—
283	C₂²	C₂×#99×C₄₇	1	2	yes	—
284	C₂²	C₂×#100×C₄₇	1	2	yes	—
285	C₄	—	2	4	no	—
286	C₄	—	2	4	no	—
287	C₄	—	4	4	no	—
288	C₂	—	2	4	no	—
289	C₂	—	4	4	no	—
290	C₂	—	8	4	no	—
291	C₂	C₄₇×#1471	1	4	yes	—
292	C₂	C₄₇×#1780	1	1	yes	characteristic
293	C₂	C₄₇×#1781	1	1	yes	characteristic
294	C₂	C₄₇×#1783	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#121×C₄₇

C₂

yes

maximal, characteristic

C₄₇×#1779

C₂

yes

maximal, complemented

C₂×C₄₇×#323

C₂

yes

maximal, complemented

C₂³×D₄×C₄₇

C₄

yes

characteristic

C₂³×D₄×C₄₇

C₄

yes

—

C₂⁴×C₄×C₄₇

C₂²

yes

characteristic

C₂×#121×C₄₇

—

C₂×#121×C₄₇

—

C₂²×C₄⋊C₄×C₄₇

C₄

yes

characteristic

C₂²×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₈×C₄₇

—

C₂×C₂²⋊C₈×C₄₇

C₂²

yes

—

C₄₇×#323

—

C₂⁵×C₄₇

C₂×C₄

yes

characteristic

C₂⁵×C₄₇

C₂×C₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

D₄

yes

—

C₂³×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₈×C₄₇

—

#121×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

D₄

yes

—

C₂²⋊C₈×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂⁴×C₄₇

C₂²×C₄

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#100

yes

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

—

100

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

101

C₂³×C₄₇

#131

yes

—

102

D₄×C₄₇

—

103

D₄×C₄₇

—

104

C₂×C₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

—

109

C₂×C₄×C₄₇

—

110

C₂×C₄×C₄₇

—

111

C₂×C₄×C₄₇

—

112

C₂×C₄×C₄₇

—

113

C₂×C₄×C₄₇

—

114

C₂×C₄×C₄₇

#99

yes

—

115

C₂×C₄×C₄₇

#120

yes

—

116

C₈×C₄₇

—

117

#8307

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

—

125

C₂²×C₄₇

—

126

C₂²×C₄₇

—

127

C₂²×C₄₇

—

128

C₂²×C₄₇

—

129

C₂²×C₄₇

—

130

C₂²×C₄₇

—

131

C₂²×C₄₇

—

132

C₂²×C₄₇

—

133

C₂²×C₄₇

#379

yes

characteristic

134

C₂²×C₄₇

#408

yes

—

135

C₂²×C₄₇

#408

yes

—

136

C₂²×C₄₇

C₂×#99

yes

—

137

C₂²×C₄₇

C₂×#100

yes

—

138

C₄×C₄₇

—

139

C₄×C₄₇

—

140

C₄×C₄₇

—

141

C₂²×#121

C₂×C₄₇

yes

characteristic

142

#1779

C₂×C₄₇

yes

complemented

143

C₂×#323

C₂×C₄₇

yes

complemented

144

C₂×C₄₇

—

145

C₂×C₄₇

—

146

C₂×C₄₇

—

147

C₂×C₄₇

#1471

yes

—

148

C₂×C₄₇

#1780

yes

characteristic

149

C₂×C₄₇

#1781

yes

characteristic

150

C₂×C₄₇

#1783

yes

characteristic

151

C₂³×D₄

C₄×C₄₇

yes

characteristic

152

C₂³×D₄

C₄×C₄₇

yes

—

153

C₂⁴×C₄

C₂²×C₄₇

yes

characteristic

154

C₂×#121

—

155

C₂×#121

—

156

C₂²×C₄⋊C₄

C₄×C₄₇

yes

characteristic

157

C₂²×C₂²⋊C₄

C₂²×C₄₇

yes

—

158

C₂×C₂²⋊C₈

—

159

C₂×C₂²⋊C₈

C₂²×C₄₇

yes

—

160

#323

—

161

C₄₇

#8307

yes

characteristic, direct product factor, Sylow

162

C₂⁵

C₂×C₄×C₄₇

yes

characteristic

163

C₂⁵

C₂×C₄×C₄₇

yes

—

164

C₂²×D₄

—

165

C₂²×D₄

—

166

C₂²×D₄

—

167

C₂²×D₄

—

168

C₂²×D₄

—

169

C₂²×D₄

—

170

C₂²×D₄

—

171

C₂³×C₄

—

172

C₂³×C₄

—

173

C₂³×C₄

C₂×C₄×C₄₇

yes

characteristic

174

C₂³×C₄

C₂×C₄×C₄₇

yes

—

175

C₂³×C₄

D₄×C₄₇

yes

—

176

C₂³×C₄

C₂³×C₄₇

yes

characteristic

177

C₂²×C₈

—

178

#121

—

179

C₂×C₄⋊C₄

—

180

C₂×C₄⋊C₄

—

181

C₂×C₂²⋊C₄

—

182

C₂×C₂²⋊C₄

—

183

C₂×C₂²⋊C₄

D₄×C₄₇

yes

—

184

C₂²⋊C₈

—

185

C₂²⋊C₈

—

186

C₂⁴

—

187

C₂⁴

—

188

C₂⁴

—

189

C₂⁴

—

190

C₂⁴

—

191

C₂⁴

—

192

C₂⁴

—

193

C₂⁴

—

194

C₂⁴

—

195

C₂⁴

C₂²⋊C₄×C₄₇

yes

—

196

C₂⁴

C₂²⋊C₄×C₄₇

yes

—

197

C₂⁴

C₂²×C₄×C₄₇

yes

characteristic

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

209

C₂²×C₄

—

210

C₂²×C₄

—

211

C₂²×C₄

—

212

C₂²×C₄

—

213

C₂²×C₄

—

214

C₂²×C₄

—

215

C₂²×C₄

—

216

C₂²×C₄

—

217

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

218

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

219

C₂²×C₄

C₂×D₄×C₄₇

yes

—

220

C₂²×C₄

C₂×D₄×C₄₇

yes

—

221

C₂×C₈

—

222

C₂×C₈

—

223

C₄⋊C₄

—

224

C₂²⋊C₄

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

—

240

C₂³

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

246

C₂³

#100×C₄₇

yes

—

247

C₂³

C₂×C₂²⋊C₄×C₄₇

yes

—

248

C₂³

C₂×C₂²⋊C₄×C₄₇

yes

characteristic

249

C₂³

#131×C₄₇

yes

—

250

D₄

—

251

D₄

—

252

C₂×C₄

—

253

C₂×C₄

—

254

C₂×C₄

—

255

C₂×C₄

—

256

C₂×C₄

—

257

C₂×C₄

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

#99×C₄₇

yes

—

263

C₂×C₄

#120×C₄₇

yes

—

264

C₈

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

—

272

C₂²

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

279

C₂²

—

280

C₂²

C₄₇×#379

yes

characteristic

281

C₂²

C₄₇×#408

yes

—

282

C₂²

C₄₇×#408

yes

—

283

C₂²

C₂×#99×C₄₇

yes

—

284

C₂²

C₂×#100×C₄₇

yes

—

285

C₄

—

286

C₄

—

287

C₄

—

288

C₂

—

289

C₂

—

290

C₂

—

291

C₂

C₄₇×#1471

yes

—

292

C₂

C₄₇×#1780

yes

characteristic

293

C₂

C₄₇×#1781

yes

characteristic

294

C₂

C₄₇×#1783

yes

characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂²×#121×C₄₇	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂³×C₄₇

C₂×C₂²⋊C₄

commutator

C₂⁴

C₂²×C₄×C₄₇

Frattini, cosocle

C₂³×C₄

C₂³×C₄₇

prime radical

C₂²×#121×C₄₇

C₂

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

N	H ≅ G/N	type
2. C₄₇×#1779	C₂	semidirect
3. C₂×C₄₇×#323	C₂	semidirect
117. #8307	C₄₇	direct (N × H)
142. #1779	C₂×C₄₇	semidirect
143. C₂×#323	C₂×C₄₇	semidirect
161. C₄₇	#8307	direct (N × H)

H ≅ G/N

type

2. C₄₇×#1779

C₂

semidirect

3. C₂×C₄₇×#323

C₂

semidirect

117. #8307

C₄₇

direct (N × H)

142. #1779

C₂×C₄₇

semidirect

143. C₂×#323

C₂×C₄₇

semidirect

161. C₄₇

#8307

direct (N × H)

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

subgroup	index
C₂²×#121×C₄₇	2
C₄₇×#1779	2
C₂×C₄₇×#323	2
#8307	47

subgroup

index

C₂²×#121×C₄₇

C₄₇×#1779

C₂×C₄₇×#323

#8307

Subgroups — C₄₇×#8307 #26048005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#8307 #26048005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8307 #26048005