Group #26048250 — subgroups

Subgroups — C₄₇×#8552 #26048250

Order 12032.

1154 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 158 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×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1784	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1462	C₂	1	4	yes	maximal, complemented
4	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
5	C₂³×D₄×C₄₇	C₄	1	1	yes	characteristic
6	C₂×#124×C₄₇	—	2	4	no	—
7	C₂×#124×C₄₇	—	2	8	no	—
8	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
9	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₇	C₄	1	1	yes	characteristic
11	C₂×#101×C₄₇	—	2	4	no	—
12	C₄₇×#407	C₂²	1	4	yes	—
13	C₄₇×#323	—	2	8	no	—
14	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
15	C₂²×Q₈×C₄₇	—	2	4	no	—
16	C₂²×Q₈×C₄₇	—	4	4	no	—
17	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
18	C₂²×D₄×C₄₇	—	2	4	no	—
19	C₂²×D₄×C₄₇	—	2	2	no	—
20	C₂²×D₄×C₄₇	—	4	4	no	—
21	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×M₁₆×C₄₇	—	2	4	no	—
26	#124×C₄₇	—	2	32	no	—
27	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
28	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
30	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
31	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
32	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	—
33	C₂×C₄²×C₄₇	—	2	4	no	—
34	C₂×C₄²×C₄₇	—	2	2	no	—
35	#101×C₄₇	—	4	8	no	—
36	C₂²⋊C₈×C₄₇	—	2	8	no	—
37	C₂⁴×C₄₇	—	2	2	no	—
38	C₂⁴×C₄₇	—	2	2	no	—
39	C₂⁴×C₄₇	—	4	4	no	—
40	C₂⁴×C₄₇	—	4	4	no	—
41	C₂⁴×C₄₇	—	4	4	no	—
42	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
43	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
44	C₂×Q₈×C₄₇	—	2	8	no	—
45	C₂×Q₈×C₄₇	—	2	8	no	—
46	C₂×Q₈×C₄₇	—	4	4	no	—
47	C₂×Q₈×C₄₇	—	4	16	no	—
48	C₂×D₄×C₄₇	—	2	8	no	—
49	C₂×D₄×C₄₇	—	4	16	no	—
50	C₂×D₄×C₄₇	—	4	4	no	—
51	C₂×D₄×C₄₇	—	4	4	no	—
52	C₂²×C₄×C₄₇	—	2	2	no	—
53	C₂²×C₄×C₄₇	—	2	4	no	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	4	2	no	—
58	C₂²×C₄×C₄₇	—	4	2	no	—
59	C₂²×C₄×C₄₇	—	4	4	no	—
60	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
63	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
65	M₁₆×C₄₇	—	4	8	no	—
66	C₂×C₈×C₄₇	—	4	4	no	—
67	C₂²⋊C₄×C₄₇	—	2	16	no	—
68	C₂²⋊C₄×C₄₇	—	2	16	no	—
69	C₄²×C₄₇	—	2	8	no	—
70	C₂³×C₄₇	—	2	2	no	—
71	C₂³×C₄₇	—	2	4	no	—
72	C₂³×C₄₇	—	2	4	no	—
73	C₂³×C₄₇	—	2	8	no	—
74	C₂³×C₄₇	—	4	4	no	—
75	C₂³×C₄₇	—	4	4	no	—
76	C₂³×C₄₇	—	4	4	no	—
77	C₂³×C₄₇	—	4	4	no	—
78	C₂³×C₄₇	—	4	4	no	—
79	C₂³×C₄₇	—	4	4	no	—
80	C₂³×C₄₇	—	4	4	no	—
81	C₂³×C₄₇	—	4	4	no	—
82	C₂³×C₄₇	—	8	16	no	—
83	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
85	Q₈×C₄₇	—	4	16	no	—
86	D₄×C₄₇	—	4	16	no	—
87	C₂×C₄×C₄₇	—	2	8	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	—	2	4	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	4	no	—
92	C₂×C₄×C₄₇	—	2	2	no	—
93	C₂×C₄×C₄₇	—	2	4	no	—
94	C₂×C₄×C₄₇	—	4	4	no	—
95	C₂×C₄×C₄₇	—	4	4	no	—
96	C₂×C₄×C₄₇	—	4	4	no	—
97	C₂×C₄×C₄₇	—	4	4	no	—
98	C₂×C₄×C₄₇	—	4	4	no	—
99	C₂×C₄×C₄₇	#99	1	4	yes	—
100	C₂×C₄×C₄₇	#120	1	4	yes	—
101	C₈×C₄₇	—	8	4	no	—
102	#8552	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂²×C₄₇	—	2	8	no	—
104	C₂²×C₄₇	—	2	2	no	—
105	C₂²×C₄₇	—	2	2	no	—
106	C₂²×C₄₇	—	2	2	no	—
107	C₂²×C₄₇	—	4	4	no	—
108	C₂²×C₄₇	—	4	4	no	—
109	C₂²×C₄₇	—	4	4	no	—
110	C₂²×C₄₇	—	8	8	no	—
111	C₂²×C₄₇	—	8	8	no	—
112	C₂²×C₄₇	—	8	8	no	—
113	C₂²×C₄₇	#379	1	1	yes	characteristic
114	C₂²×C₄₇	C₂×#99	1	2	yes	—
115	C₂²×C₄₇	#413	1	4	yes	—
116	C₄×C₄₇	—	2	4	no	—
117	C₄×C₄₇	—	2	4	no	—
118	C₄×C₄₇	—	4	2	no	—
119	C₄×C₄₇	—	4	4	no	—
120	C₂²×#124	C₂×C₄₇	1	1	yes	characteristic
121	#1784	C₂×C₄₇	1	2	yes	complemented
122	#1462	C₂×C₄₇	1	4	yes	complemented
123	C₂×C₄₇	—	2	2	no	—
124	C₂×C₄₇	—	2	4	no	—
125	C₂×C₄₇	—	8	4	no	—
126	C₂×C₄₇	#1781	1	1	yes	characteristic
127	C₂×C₄₇	#1785	1	2	yes	—
128	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
129	C₂³×D₄	C₄×C₄₇	1	1	yes	characteristic
130	C₂×#124	—	2	4	no	—
131	C₂×#124	—	2	8	no	—
132	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
133	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
134	C₂²×C₄²	C₄×C₄₇	1	1	yes	characteristic
135	C₂×#101	—	2	4	no	—
136	#407	C₂²×C₄₇	1	4	yes	—
137	#323	—	2	8	no	—
138	C₄₇	#8552	1	1	yes	characteristic, direct product factor, Sylow
139	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
140	C₂²×Q₈	—	2	4	no	—
141	C₂²×Q₈	—	4	4	no	—
142	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
143	C₂²×D₄	—	2	4	no	—
144	C₂²×D₄	—	2	2	no	—
145	C₂²×D₄	—	4	4	no	—
146	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
147	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
148	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
149	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
150	C₂×M₁₆	—	2	4	no	—
151	#124	—	2	32	no	—
152	C₂×C₂²⋊C₄	—	2	4	no	—
153	C₂×C₂²⋊C₄	—	2	4	no	—
154	C₂×C₂²⋊C₄	—	2	4	no	—
155	C₂×C₂²⋊C₄	—	2	4	no	—
156	C₂×C₂²⋊C₄	—	2	4	no	—
157	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	—
158	C₂×C₄²	—	2	4	no	—
159	C₂×C₄²	—	2	2	no	—
160	#101	—	4	8	no	—
161	C₂²⋊C₈	—	2	8	no	—
162	C₂⁴	—	2	2	no	—
163	C₂⁴	—	2	2	no	—
164	C₂⁴	—	4	4	no	—
165	C₂⁴	—	4	4	no	—
166	C₂⁴	—	4	4	no	—
167	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
168	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
169	C₂×Q₈	—	2	8	no	—
170	C₂×Q₈	—	2	8	no	—
171	C₂×Q₈	—	4	4	no	—
172	C₂×Q₈	—	4	16	no	—
173	C₂×D₄	—	2	8	no	—
174	C₂×D₄	—	4	16	no	—
175	C₂×D₄	—	4	4	no	—
176	C₂×D₄	—	4	4	no	—
177	C₂²×C₄	—	2	2	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	2	no	—
184	C₂²×C₄	—	4	4	no	—
185	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
186	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
187	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
188	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
189	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
190	M₁₆	—	4	8	no	—
191	C₂×C₈	—	4	4	no	—
192	C₂²⋊C₄	—	2	16	no	—
193	C₂²⋊C₄	—	2	16	no	—
194	C₄²	—	2	8	no	—
195	C₂³	—	2	2	no	—
196	C₂³	—	2	4	no	—
197	C₂³	—	2	4	no	—
198	C₂³	—	2	8	no	—
199	C₂³	—	4	4	no	—
200	C₂³	—	4	4	no	—
201	C₂³	—	4	4	no	—
202	C₂³	—	4	4	no	—
203	C₂³	—	4	4	no	—
204	C₂³	—	4	4	no	—
205	C₂³	—	4	4	no	—
206	C₂³	—	4	4	no	—
207	C₂³	—	8	16	no	—
208	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
209	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
210	Q₈	—	4	16	no	—
211	D₄	—	4	16	no	—
212	C₂×C₄	—	2	8	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	—	4	4	no	—
223	C₂×C₄	—	4	4	no	—
224	C₂×C₄	#99×C₄₇	1	4	yes	—
225	C₂×C₄	#120×C₄₇	1	4	yes	—
226	C₈	—	8	4	no	—
227	C₂²	—	2	8	no	—
228	C₂²	—	2	2	no	—
229	C₂²	—	2	2	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	4	4	no	—
232	C₂²	—	4	4	no	—
233	C₂²	—	4	4	no	—
234	C₂²	—	8	8	no	—
235	C₂²	—	8	8	no	—
236	C₂²	—	8	8	no	—
237	C₂²	C₄₇×#379	1	1	yes	characteristic
238	C₂²	C₂×#99×C₄₇	1	2	yes	—
239	C₂²	C₄₇×#413	1	4	yes	—
240	C₄	—	2	4	no	—
241	C₄	—	2	4	no	—
242	C₄	—	4	2	no	—
243	C₄	—	4	4	no	—
244	C₂	—	2	2	no	—
245	C₂	—	2	4	no	—
246	C₂	—	8	4	no	—
247	C₂	C₄₇×#1781	1	1	yes	characteristic
248	C₂	C₄₇×#1785	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#124×C₄₇

C₂

yes

maximal, characteristic

C₄₇×#1784

C₂

yes

maximal, complemented

C₄₇×#1462

C₂

yes

maximal, complemented

C₂³×Q₈×C₄₇

C₂²

yes

characteristic

C₂³×D₄×C₄₇

C₄

yes

characteristic

C₂×#124×C₄₇

—

C₂×#124×C₄₇

—

C₂²×C₂²⋊C₄×C₄₇

C₄

yes

—

C₂²×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂²×C₄²×C₄₇

C₄

yes

characteristic

C₂×#101×C₄₇

—

C₄₇×#407

C₂²

yes

—

C₄₇×#323

—

C₂⁵×C₄₇

C₂×C₄

yes

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

D₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂×C₄

yes

—

C₂³×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂³×C₄×C₄₇

C₂³

yes

characteristic

C₂×M₁₆×C₄₇

—

#124×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

—

C₂×C₂²⋊C₄×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

—

#101×C₄₇

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

—

C₂⁴×C₄₇

C₂²⋊C₄

yes

—

C₂⁴×C₄₇

C₂²×C₄

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×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

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×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

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

—

Q₈×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#99

yes

—

100

C₂×C₄×C₄₇

#120

yes

—

101

C₈×C₄₇

—

102

#8552

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

—

112

C₂²×C₄₇

—

113

C₂²×C₄₇

#379

yes

characteristic

114

C₂²×C₄₇

C₂×#99

yes

—

115

C₂²×C₄₇

#413

yes

—

116

C₄×C₄₇

—

117

C₄×C₄₇

—

118

C₄×C₄₇

—

119

C₄×C₄₇

—

120

C₂²×#124

C₂×C₄₇

yes

characteristic

121

#1784

C₂×C₄₇

yes

complemented

122

#1462

C₂×C₄₇

yes

complemented

123

C₂×C₄₇

—

124

C₂×C₄₇

—

125

C₂×C₄₇

—

126

C₂×C₄₇

#1781

yes

characteristic

127

C₂×C₄₇

#1785

yes

—

128

C₂³×Q₈

C₂²×C₄₇

yes

characteristic

129

C₂³×D₄

C₄×C₄₇

yes

characteristic

130

C₂×#124

—

131

C₂×#124

—

132

C₂²×C₂²⋊C₄

C₄×C₄₇

yes

—

133

C₂²×C₂²⋊C₄

C₂²×C₄₇

yes

—

134

C₂²×C₄²

C₄×C₄₇

yes

characteristic

135

C₂×#101

—

136

#407

C₂²×C₄₇

yes

—

137

#323

—

138

C₄₇

#8552

yes

characteristic, direct product factor, Sylow

139

C₂⁵

C₂×C₄×C₄₇

yes

—

140

C₂²×Q₈

—

141

C₂²×Q₈

—

142

C₂²×Q₈

D₄×C₄₇

yes

—

143

C₂²×D₄

—

144

C₂²×D₄

—

145

C₂²×D₄

—

146

C₂³×C₄

C₂×C₄×C₄₇

yes

characteristic

147

C₂³×C₄

C₂×C₄×C₄₇

yes

characteristic

148

C₂³×C₄

C₂×C₄×C₄₇

yes

—

149

C₂³×C₄

C₂³×C₄₇

yes

characteristic

150

C₂×M₁₆

—

151

#124

—

152

C₂×C₂²⋊C₄

—

153

C₂×C₂²⋊C₄

—

154

C₂×C₂²⋊C₄

—

155

C₂×C₂²⋊C₄

—

156

C₂×C₂²⋊C₄

—

157

C₂×C₂²⋊C₄

D₄×C₄₇

yes

—

158

C₂×C₄²

—

159

C₂×C₄²

—

160

#101

—

161

C₂²⋊C₈

—

162

C₂⁴

—

163

C₂⁴

—

164

C₂⁴

—

165

C₂⁴

—

166

C₂⁴

—

167

C₂⁴

C₂²⋊C₄×C₄₇

yes

—

168

C₂⁴

C₂²×C₄×C₄₇

yes

characteristic

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

—

185

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

186

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

187

C₂²×C₄

C₂²⋊C₄×C₄₇

yes

—

188

C₂²×C₄

C₂×D₄×C₄₇

yes

—

189

C₂²×C₄

C₂×D₄×C₄₇

yes

—

190

M₁₆

—

191

C₂×C₈

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

194

C₄²

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

—

208

C₂³

C₂×C₂²⋊C₄×C₄₇

yes

characteristic

209

C₂³

C₂×C₂²⋊C₄×C₄₇

yes

—

210

Q₈

—

211

D₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

#99×C₄₇

yes

—

225

C₂×C₄

#120×C₄₇

yes

—

226

C₈

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

C₄₇×#379

yes

characteristic

238

C₂²

C₂×#99×C₄₇

yes

—

239

C₂²

C₄₇×#413

yes

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₂

—

245

C₂

—

246

C₂

—

247

C₂

C₄₇×#1781

yes

characteristic

248

C₂

C₄₇×#1785

yes

—

	subgroup	G/H
center, socle	C₂²×C₄₇	#379
commutator	C₂⁴	C₂²×C₄×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂³×D₄×C₄₇	C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₄₇

#379

commutator

C₂⁴

C₂²×C₄×C₄₇

Frattini, cosocle

C₂³×C₄

C₂³×C₄₇

prime radical

C₂³×D₄×C₄₇

C₄

LCS

G ▷ C₂⁴ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

N	H ≅ G/N	type
2. C₄₇×#1784	C₂	semidirect
3. C₄₇×#1462	C₂	semidirect
102. #8552	C₄₇	direct (N × H)
121. #1784	C₂×C₄₇	semidirect
122. #1462	C₂×C₄₇	semidirect
138. C₄₇	#8552	direct (N × H)

H ≅ G/N

type

2. C₄₇×#1784

C₂

semidirect

3. C₄₇×#1462

C₂

semidirect

102. #8552

C₄₇

direct (N × H)

121. #1784

C₂×C₄₇

semidirect

122. #1462

C₂×C₄₇

semidirect

138. C₄₇

#8552

direct (N × H)

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

subgroup	index
C₂²×#124×C₄₇	2
C₄₇×#1784	2
C₄₇×#1462	2
#8552	47

subgroup

index

C₂²×#124×C₄₇

C₄₇×#1784

C₄₇×#1462

#8552

Subgroups — C₄₇×#8552 #26048250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#8552 #26048250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8552 #26048250