Group #28505258 — subgroups

Subgroups — #28505258

Order 15104.

408 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 135 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	C₂×#16837451	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837225	C₂	1	2	yes	maximal, complemented
3	#21424129	C₂	1	1	yes	maximal, characteristic
4	#21422205	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#349	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11745664	—	2	1	no	—
7	#16837451	—	2	4	no	—
8	C₂×#14273663	—	2	1	no	—
9	C₂×#14273663	C₂²	1	2	yes	—
10	C₂×#14273661	C₂²	1	1	yes	characteristic
11	C₂×#14273659	C₂²	1	1	yes	characteristic
12	#16837262	—	2	1	no	—
13	#16837225	—	2	4	no	—
14	#16837165	—	2	1	no	—
15	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₅₉	C₂²	1	2	yes	—
17	C₅₉×#349	C₄	1	4	yes	complemented
18	C₂×#11745664	—	2	4	no	—
19	C₂×#11745664	—	2	2	no	—
20	C₂×#11745664	—	4	1	no	—
21	C₂×#11745664	—	4	2	no	—
22	C₂²×C₅₉⋊C₈	—	4	1	no	—
23	C₂×C₄⋊Dic₅₉	—	2	1	no	—
24	C₂×C₄⋊Dic₅₉	—	2	1	no	—
25	C₂×C₂²⋊Dic₅₉	—	4	1	no	—
26	#14273663	—	2	4	no	—
27	#14273663	—	2	2	no	—
28	#14273663	D₄	1	4	yes	—
29	#14273661	—	2	2	no	—
30	#14273659	—	2	2	no	—
31	C₅₉⋊#95	—	4	1	no	—
32	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
33	C₂×M₁₆×C₅₉	—	2	2	no	—
34	C₂×M₁₆×C₅₉	—	2	2	no	—
35	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
36	C₂×M₁₆×C₅₉	Q₈	1	2	yes	—
37	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
39	M₃₂×C₅₉	—	2	2	no	—
40	M₃₂×C₅₉	C₂×C₄	1	4	yes	—
41	C₂×C₁₆×C₅₉	—	2	2	no	—
42	C₂⁴×C₅₉	SD₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₅₉	—	2	1	no	—
44	C₂²×C₄×C₅₉	—	2	1	no	—
45	C₂²×C₄×C₅₉	—	2	1	no	—
46	C₂²×C₄×C₅₉	—	2	1	no	—
47	C₂²×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₅₉	SD₁₆	1	1	yes	characteristic
49	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
50	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₅₉	—	4	1	no	—
52	C₂²×Dic₅₉	—	4	1	no	—
53	M₁₆×C₅₉	—	2	4	no	—
54	M₁₆×C₅₉	—	2	4	no	—
55	C₂×C₈×C₅₉	—	2	1	no	—
56	C₂×C₈×C₅₉	—	2	1	no	—
57	C₂×C₈×C₅₉	C₄⋊C₄	1	2	yes	—
58	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
61	C₂×C₈×C₅₉	#41	1	2	yes	—
62	C₂²⋊Dic₅₉	—	8	2	no	—
63	C₄⋊Dic₅₉	—	4	1	no	—
64	C₄⋊Dic₅₉	—	4	1	no	—
65	C₄⋊Dic₅₉	—	4	1	no	—
66	C₄⋊Dic₅₉	—	4	1	no	—
67	#11745664	—	2	4	no	—
68	#11745664	—	4	4	no	—
69	#11745664	—	4	2	no	—
70	C₂×C₅₉⋊C₈	—	4	4	no	—
71	C₂×C₅₉⋊C₈	—	4	2	no	—
72	C₁₆×C₅₉	—	2	4	no	—
73	C₂³×C₅₉	—	2	1	no	—
74	C₂³×C₅₉	—	2	1	no	—
75	C₂³×C₅₉	—	4	1	no	—
76	C₂³×C₅₉	—	4	1	no	—
77	C₂³×C₅₉	#106	1	2	yes	—
78	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₅₉	—	2	1	no	—
80	C₂×C₄×C₅₉	—	2	1	no	—
81	C₂×C₄×C₅₉	—	2	2	no	—
82	C₂×C₄×C₅₉	—	2	2	no	—
83	C₂×C₄×C₅₉	—	2	2	no	—
84	C₂×C₄×C₅₉	—	2	2	no	—
85	C₂×C₄×C₅₉	#106	1	2	yes	—
86	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
90	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
92	C₂×Dic₅₉	—	8	1	no	—
93	C₂×Dic₅₉	—	8	1	no	—
94	C₂×Dic₅₉	—	8	1	no	—
95	C₂×Dic₅₉	—	8	1	no	—
96	C₂×Dic₅₉	—	8	1	no	—
97	C₂×Dic₅₉	—	8	1	no	—
98	C₈×C₅₉	—	2	2	no	—
99	C₈×C₅₉	C₄×D₄	1	2	yes	—
100	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
101	C₅₉⋊C₈	—	4	4	no	—
102	#12931	—	59	1	no	maximal, Sylow
103	C₂²×C₅₉	—	2	1	no	—
104	C₂²×C₅₉	—	2	1	no	—
105	C₂²×C₅₉	—	2	2	no	—
106	C₂²×C₅₉	—	4	2	no	—
107	C₂²×C₅₉	—	4	1	no	—
108	C₂²×C₅₉	—	4	1	no	—
109	C₂²×C₅₉	—	8	1	no	—
110	C₂²×C₅₉	C₂×#106	1	1	yes	characteristic
111	C₂²×C₅₉	#448	1	1	yes	characteristic
112	C₂²×C₅₉	#481	1	1	yes	characteristic
113	C₄×C₅₉	—	2	2	no	—
114	C₄×C₅₉	#385	1	1	yes	characteristic
115	C₄×C₅₉	#428	1	1	yes	characteristic
116	C₄×C₅₉	#450	1	1	yes	characteristic
117	C₄×C₅₉	#483	1	1	yes	characteristic
118	Dic₅₉	—	16	1	no	—
119	Dic₅₉	—	16	1	no	—
120	C₂×#430	—	59	1	no	—
121	C₂×#365	—	59	2	no	—
122	C₂×#349	D₅₉	1	1	yes	characteristic
123	#1809	—	59	1	no	—
124	#1387	—	59	2	no	—
125	C₂×C₅₉	—	2	1	no	—
126	C₂×C₅₉	—	2	1	no	—
127	C₂×C₅₉	—	4	2	no	—
128	C₂×C₅₉	#1853	1	1	yes	characteristic
129	C₂×C₅₉	#2238	1	1	yes	characteristic
130	C₂×C₅₉	#2239	1	1	yes	characteristic
131	C₂²×M₁₆	—	118	1	no	—
132	C₂²×M₁₆	C₂×D₅₉	1	1	yes	characteristic
133	C₂×M₃₂	C₂×D₅₉	1	2	yes	—
134	#430	—	118	4	no	—
135	C₂×#108	—	59	2	no	—
136	C₂×#108	—	118	1	no	—
137	C₂×#107	—	59	1	no	—
138	C₂×#106	—	59	1	no	—
139	#380	—	118	1	no	—
140	#365	—	118	4	no	—
141	#349	Dic₅₉	1	4	yes	complemented
142	#340	—	118	1	no	—
143	C₅₉	#12931	1	1	yes	characteristic, complemented, Sylow
144	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
145	C₂×M₁₆	—	2	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	118	4	no	—
148	C₂×M₁₆	—	118	2	no	—
149	C₂×M₁₆	—	236	1	no	—
150	C₂×M₁₆	—	236	2	no	—
151	C₂×M₁₆	Dic₁₁₈	1	2	yes	—
152	C₂×M₁₆	C₂×Dic₅₉	1	2	yes	—
153	C₂²×C₈	—	236	1	no	—
154	C₂²×C₈	D₂₃₆	1	1	yes	characteristic
155	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
156	C₂×C₄⋊C₄	—	118	1	no	—
157	C₂×C₄⋊C₄	—	118	1	no	—
158	C₂×C₂²⋊C₄	—	236	1	no	—
159	M₃₂	—	2	2	no	—
160	M₃₂	C₂×Dic₅₉	1	4	yes	—
161	C₂×C₁₆	—	2	2	no	—
162	#108	—	59	4	no	—
163	#108	—	118	4	no	—
164	#108	—	118	2	no	—
165	#107	—	118	2	no	—
166	#106	—	118	2	no	—
167	#95	—	236	1	no	—
168	C₂⁴	#11745660	1	1	yes	characteristic
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	2	1	no	—
173	C₂²×C₄	—	236	1	no	—
174	C₂²×C₄	—	236	1	no	—
175	C₂²×C₄	#11745660	1	1	yes	characteristic
176	C₂²×C₄	#11745660	1	2	yes	—
177	C₂²×C₄	C₄⋊Dic₅₉	1	2	yes	—
178	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
179	M₁₆	—	2	4	no	—
180	M₁₆	—	2	4	no	—
181	M₁₆	—	118	4	no	—
182	M₁₆	—	236	4	no	—
183	M₁₆	—	236	2	no	—
184	C₂×C₈	—	2	1	no	—
185	C₂×C₈	—	2	1	no	—
186	C₂×C₈	—	236	4	no	—
187	C₂×C₈	—	236	2	no	—
188	C₂×C₈	C₄⋊Dic₅₉	1	2	yes	—
189	C₂×C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
190	C₂×C₈	D₄×D₅₉	1	2	yes	—
191	C₂×C₈	#11745687	1	2	yes	—
192	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
193	C₄⋊C₄	—	236	1	no	—
194	C₄⋊C₄	—	236	1	no	—
195	C₄⋊C₄	—	236	1	no	—
196	C₄⋊C₄	—	236	1	no	—
197	C₂²⋊C₄	—	472	2	no	—
198	C₁₆	—	2	4	no	—
199	C₂³	—	2	1	no	—
200	C₂³	—	2	1	no	—
201	C₂³	—	4	1	no	—
202	C₂³	—	4	1	no	—
203	C₂³	#14273659	1	2	yes	—
204	C₂³	C₂×#11745660	1	1	yes	characteristic
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	472	1	no	—
212	C₂×C₄	—	472	1	no	—
213	C₂×C₄	—	472	1	no	—
214	C₂×C₄	—	472	1	no	—
215	C₂×C₄	—	472	1	no	—
216	C₂×C₄	—	472	1	no	—
217	C₂×C₄	#14273659	1	2	yes	—
218	C₂×C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
219	C₂×C₄	#14273697	1	1	yes	characteristic
220	C₂×C₄	#14273711	1	1	yes	characteristic
221	C₂×C₄	C₂×#11745660	1	1	yes	characteristic
222	C₂×C₄	#14273755	1	1	yes	characteristic
223	C₂×C₄	#14273760	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	236	4	no	—
226	C₈	D₄×Dic₅₉	1	2	yes	—
227	C₈	#14273704	1	2	yes	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	4	2	no	—
232	C₂²	—	4	1	no	—
233	C₂²	—	4	1	no	—
234	C₂²	—	8	1	no	—
235	C₂²	C₂×#14273659	1	1	yes	characteristic
236	C₂²	#16837543	1	1	yes	characteristic
237	C₂²	#16837721	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	944	1	no	—
240	C₄	—	944	1	no	—
241	C₄	#16837277	1	1	yes	characteristic
242	C₄	#16837444	1	1	yes	characteristic
243	C₄	#16837555	1	1	yes	characteristic
244	C₄	#16837733	1	1	yes	characteristic
245	C₂	—	2	1	no	—
246	C₂	—	2	1	no	—
247	C₂	—	4	2	no	—
248	C₂	#21424291	1	1	yes	characteristic
249	C₂	#21426311	1	1	yes	characteristic
250	C₂	#21426316	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837451

C₂

yes

maximal, characteristic

C₂×#16837225

C₂

yes

maximal, complemented

#21424129

C₂

yes

maximal, characteristic

#21422205

C₂

yes

maximal, complemented

C₂×C₅₉×#349

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×#14273661

C₂²

yes

characteristic

C₂×#14273659

C₂²

yes

—

—

—

C₂²×M₁₆×C₅₉

C₂²

yes

characteristic

C₂×M₃₂×C₅₉

C₂²

yes

—

C₅₉×#349

C₄

yes

—

—

—

—

C₂²×C₅₉⋊C₈

—

C₂×C₄⋊Dic₅₉

—

C₂×C₄⋊Dic₅₉

—

C₂×C₂²⋊Dic₅₉

—

#14273663

—

#14273663

—

#14273663

D₄

yes

—

#14273661

—

#14273659

—

C₅₉⋊#95

—

C₂³×C₄×C₅₉

D₄

yes

characteristic

C₂×M₁₆×C₅₉

—

C₂×M₁₆×C₅₉

—

C₂×M₁₆×C₅₉

C₂×C₄

yes

—

C₂×M₁₆×C₅₉

Q₈

yes

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

C₂³

yes

characteristic

M₃₂×C₅₉

—

M₃₂×C₅₉

C₂×C₄

yes

—

C₂×C₁₆×C₅₉

—

C₂⁴×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₄⋊C₄

yes

—

C₂²×C₄×C₅₉

SD₁₆

yes

characteristic

C₂²×C₄×C₅₉

SD₁₆

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₄⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

#11745664

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₁₆×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#106

yes

—

C₂³×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#106

yes

—

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×SD₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

C₄×D₄

yes

—

100

C₈×C₅₉

C₂²⋊Q₈

yes

—

101

C₅₉⋊C₈

—

102

#12931

—

maximal, Sylow

103

C₂²×C₅₉

—

104

C₂²×C₅₉

—

105

C₂²×C₅₉

—

106

C₂²×C₅₉

—

107

C₂²×C₅₉

—

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

C₂×#106

yes

characteristic

111

C₂²×C₅₉

#448

yes

characteristic

112

C₂²×C₅₉

#481

yes

characteristic

113

C₄×C₅₉

—

114

C₄×C₅₉

#385

yes

characteristic

115

C₄×C₅₉

#428

yes

characteristic

116

C₄×C₅₉

#450

yes

characteristic

117

C₄×C₅₉

#483

yes

characteristic

118

Dic₅₉

—

119

Dic₅₉

—

120

C₂×#430

—

121

C₂×#365

—

122

C₂×#349

D₅₉

yes

characteristic

123

#1809

—

124

#1387

—

125

C₂×C₅₉

—

126

C₂×C₅₉

—

127

C₂×C₅₉

—

128

C₂×C₅₉

#1853

yes

characteristic

129

C₂×C₅₉

#2238

yes

characteristic

130

C₂×C₅₉

#2239

yes

characteristic

131

C₂²×M₁₆

—

118

—

132

C₂²×M₁₆

C₂×D₅₉

yes

characteristic

133

C₂×M₃₂

C₂×D₅₉

yes

—

134

#430

—

118

—

135

C₂×#108

—

136

C₂×#108

—

118

—

137

C₂×#107

—

138

C₂×#106

—

139

#380

—

118

—

140

#365

—

118

—

141

#349

Dic₅₉

yes

complemented

142

#340

—

118

—

143

C₅₉

#12931

yes

characteristic, complemented, Sylow

144

C₂³×C₄

D₂₃₆

yes

characteristic

145

C₂×M₁₆

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

118

—

148

C₂×M₁₆

—

118

—

149

C₂×M₁₆

—

236

—

150

C₂×M₁₆

—

236

—

151

C₂×M₁₆

Dic₁₁₈

yes

—

152

C₂×M₁₆

C₂×Dic₅₉

yes

—

153

C₂²×C₈

—

236

—

154

C₂²×C₈

D₂₃₆

yes

characteristic

155

C₂²×C₈

C₂²×D₅₉

yes

characteristic

156

C₂×C₄⋊C₄

—

118

—

157

C₂×C₄⋊C₄

—

118

—

158

C₂×C₂²⋊C₄

—

236

—

159

M₃₂

—

160

M₃₂

C₂×Dic₅₉

yes

—

161

C₂×C₁₆

—

162

#108

—

163

#108

—

118

—

164

#108

—

118

—

165

#107

—

118

—

166

#106

—

118

—

167

#95

—

236

—

168

C₂⁴

#11745660

yes

characteristic

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

236

—

174

C₂²×C₄

—

236

—

175

C₂²×C₄

#11745660

yes

characteristic

176

C₂²×C₄

#11745660

yes

—

177

C₂²×C₄

C₄⋊Dic₅₉

yes

—

178

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

179

M₁₆

—

180

M₁₆

—

181

M₁₆

—

118

—

182

M₁₆

—

236

—

183

M₁₆

—

236

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

236

—

187

C₂×C₈

—

236

—

188

C₂×C₈

C₄⋊Dic₅₉

yes

—

189

C₂×C₈

C₂×Dic₁₁₈

yes

characteristic

190

C₂×C₈

D₄×D₅₉

yes

—

191

C₂×C₈

#11745687

yes

—

192

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

193

C₄⋊C₄

—

236

—

194

C₄⋊C₄

—

236

—

195

C₄⋊C₄

—

236

—

196

C₄⋊C₄

—

236

—

197

C₂²⋊C₄

—

472

—

198

C₁₆

—

199

C₂³

—

200

C₂³

—

201

C₂³

—

202

C₂³

—

203

C₂³

#14273659

yes

—

204

C₂³

C₂×#11745660

yes

characteristic

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

472

—

212

C₂×C₄

—

472

—

213

C₂×C₄

—

472

—

214

C₂×C₄

—

472

—

215

C₂×C₄

—

472

—

216

C₂×C₄

—

472

—

217

C₂×C₄

#14273659

yes

—

218

C₂×C₄

C₂×C₄⋊Dic₅₉

yes

characteristic

219

C₂×C₄

#14273697

yes

characteristic

220

C₂×C₄

#14273711

yes

characteristic

221

C₂×C₄

C₂×#11745660

yes

characteristic

222

C₂×C₄

#14273755

yes

characteristic

223

C₂×C₄

#14273760

yes

characteristic

224

C₈

—

225

C₈

—

236

—

226

C₈

D₄×Dic₅₉

yes

—

227

C₈

#14273704

yes

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#14273659

yes

characteristic

236

C₂²

#16837543

yes

characteristic

237

C₂²

#16837721

yes

characteristic

238

C₄

—

239

C₄

—

944

—

240

C₄

—

944

—

241

C₄

#16837277

yes

characteristic

242

C₄

#16837444

yes

characteristic

243

C₄

#16837555

yes

characteristic

244

C₄

#16837733

yes

characteristic

245

C₂

—

246

C₂

—

247

C₂

—

248

C₂

#21424291

yes

characteristic

249

C₂

#21426311

yes

characteristic

250

C₂

#21426316

yes

characteristic

	subgroup	G/H
center	C₂²	#16837721
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₂×C₅₉×#349	C₂
socle	C₂²×C₅₉	#481
prime radical	C₂⁴×C₅₉	SD₁₆
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂×#349	D₅₉
hypocenter	C₅₉	#12931
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

subgroup

G/H

center

C₂²

#16837721

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₂×C₅₉×#349

C₂

socle

C₂²×C₅₉

#481

prime radical

C₂⁴×C₅₉

SD₁₆

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#349

N	H ≅ G/N	type
2. C₂×#16837225	C₂	semidirect
4. #21422205	C₂	semidirect
17. C₅₉×#349	C₄	semidirect
141. #349	Dic₅₉	semidirect
143. C₅₉	#12931	semidirect

H ≅ G/N

type

2. C₂×#16837225

C₂

semidirect

4. #21422205

C₂

semidirect

17. C₅₉×#349

C₄

semidirect

141. #349

Dic₅₉

semidirect

143. C₅₉

#12931

semidirect

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

subgroup	index
C₂×#16837451	2
C₂×#16837225	2
#21424129	2
#21422205	2
C₂×C₅₉×#349	2
#12931	59

subgroup

index

C₂×C₅₉×#349

Subgroups — #28505258

Conjugacy classes of subgroups

Complements

Maximal subgroups