Group #28507183 — subgroups

Subgroups — #28507183

Order 15104.

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

normal subgroups only

This group has 482 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	#21425852	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16837218	C₂	1	2	yes	maximal, complemented
3	C₂×#16837215	C₂	1	2	yes	maximal
4	C₄×#14273663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×#14273667	C₂²	1	2	yes	—
7	C₂×#14273663	C₂²	1	2	yes	—
8	C₄×#11745664	—	2	1	no	—
9	C₄⋊(C₅₉⋊C₁₆)	—	2	2	no	—
10	#16837218	—	2	4	no	—
11	#16837215	—	2	4	no	—
12	#16837167	—	2	1	no	—
13	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₅₉	—	2	1	no	—
15	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₅₉	—	2	1	no	—
17	C₅₉×#495	—	2	2	no	—
18	C₅₉×#495	C₄	1	4	yes	—
19	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#11745664	—	2	2	no	—
21	#14273667	—	2	2	no	—
22	#14273667	—	2	2	no	—
23	C₂×C₅₉⋊C₁₆	—	2	2	no	—
24	#14273663	—	2	2	no	—
25	#14273663	D₄	1	4	yes	—
26	#14273638	—	4	1	no	—
27	C₄×C₅₉⋊C₈	—	4	1	no	—
28	C₂²×Q₈×C₅₉	—	2	1	no	—
29	C₂²×D₄×C₅₉	—	2	1	no	—
30	C₂×Q₁₆×C₅₉	—	2	2	no	—
31	C₂×Q₁₆×C₅₉	—	2	1	no	—
32	C₂×Q₁₆×C₅₉	—	2	2	no	—
33	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
34	C₂×SD₁₆×C₅₉	—	2	4	no	—
35	C₂×SD₁₆×C₅₉	—	4	4	no	—
36	C₂×D₈×C₅₉	—	2	2	no	—
37	C₂×D₈×C₅₉	—	2	1	no	—
38	C₂×D₈×C₅₉	—	2	2	no	—
39	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
42	#124×C₅₉	—	2	4	no	—
43	#124×C₅₉	—	4	1	no	—
44	#124×C₅₉	—	4	1	no	—
45	C₂×C₂²⋊C₄×C₅₉	—	4	2	no	—
46	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₅₉	D₄	1	2	yes	—
49	C₂⁴×C₅₉	—	4	1	no	—
50	C₂×Q₈×C₅₉	—	2	2	no	—
51	C₂×Q₈×C₅₉	—	4	1	no	—
52	C₂×Q₈×C₅₉	—	4	2	no	—
53	C₂×Q₈×C₅₉	—	4	2	no	—
54	C₂×D₄×C₅₉	—	2	2	no	—
55	C₂×D₄×C₅₉	—	4	2	no	—
56	C₂×D₄×C₅₉	—	4	1	no	—
57	C₂×D₄×C₅₉	—	4	2	no	—
58	C₂²×C₄×C₅₉	—	4	1	no	—
59	C₂²×C₄×C₅₉	SD₁₆	1	2	yes	—
60	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₅₉	—	2	4	no	—
62	Q₁₆×C₅₉	—	4	1	no	—
63	Q₁₆×C₅₉	—	4	1	no	—
64	SD₁₆×C₅₉	—	4	8	no	—
65	D₈×C₅₉	—	2	4	no	—
66	D₈×C₅₉	—	4	1	no	—
67	D₈×C₅₉	—	4	1	no	—
68	C₂×C₈×C₅₉	—	2	2	no	—
69	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
70	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
72	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₅₉	#41	1	2	yes	—
74	C₂²⋊C₄×C₅₉	—	4	4	no	—
75	C₂²⋊C₄×C₅₉	—	4	4	no	—
76	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₅₉	D₈	1	1	yes	characteristic
78	C₄²×C₅₉	D₈	1	1	yes	characteristic
79	#11745664	—	2	4	no	—
80	#11745664	—	4	2	no	—
81	C₂×C₅₉⋊C₈	—	4	2	no	—
82	C₅₉⋊C₁₆	—	4	2	no	—
83	C₂³×C₅₉	—	4	2	no	—
84	C₂³×C₅₉	—	8	4	no	—
85	C₂³×C₅₉	—	8	2	no	—
86	C₂³×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
87	Q₈×C₅₉	—	4	2	no	—
88	Q₈×C₅₉	—	4	2	no	—
89	Q₈×C₅₉	—	8	2	no	—
90	D₄×C₅₉	—	4	2	no	—
91	D₄×C₅₉	—	4	2	no	—
92	D₄×C₅₉	—	8	2	no	—
93	C₂×C₄×C₅₉	—	4	2	no	—
94	C₂×C₄×C₅₉	—	4	2	no	—
95	C₂×C₄×C₅₉	—	8	2	no	—
96	C₂×C₄×C₅₉	#102	1	2	yes	—
97	C₂×C₄×C₅₉	#102	1	2	yes	—
98	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₅₉	#121	1	2	yes	—
100	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
102	C₈×C₅₉	—	2	2	no	—
103	C₈×C₅₉	C₄×D₄	1	2	yes	—
104	C₈×C₅₉	#124	1	1	yes	characteristic
105	C₈×C₅₉	#127	1	1	yes	characteristic
106	C₅₉⋊C₈	—	4	4	no	—
107	#13258	—	59	1	no	maximal, Sylow
108	C₂²×C₅₉	—	2	2	no	—
109	C₂²×C₅₉	—	8	4	no	—
110	C₂²×C₅₉	—	8	2	no	—
111	C₂²×C₅₉	—	16	4	no	—
112	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
113	C₂²×C₅₉	#460	1	2	yes	—
114	C₄×C₅₉	—	2	2	no	—
115	C₄×C₅₉	—	2	2	no	—
116	C₄×C₅₉	—	8	2	no	—
117	C₄×C₅₉	#390	1	1	yes	characteristic
118	C₄×C₅₉	#418	1	1	yes	characteristic
119	C₄×C₅₉	#459	1	2	yes	—
120	C₂×#495	D₅₉	1	1	yes	characteristic
121	#2150	—	59	1	no	—
122	C₂×#362	—	59	2	no	—
123	C₂×#361	—	59	2	no	—
124	C₄×#108	—	59	1	no	—
125	C₂×C₅₉	—	2	2	no	—
126	C₂×C₅₉	—	16	2	no	—
127	C₂×C₅₉	#1982	1	1	yes	characteristic
128	C₂×C₅₉	#2148	1	2	yes	—
129	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
130	C₂²×SD₁₆	—	2	1	no	—
131	C₂²×D₈	C₂×D₅₉	1	1	yes	characteristic
132	C₂×#124	—	2	1	no	—
133	C₂×M₃₂	—	59	2	no	—
134	#495	—	2	2	no	—
135	#495	Dic₅₉	1	4	yes	—
136	C₂×#108	—	59	2	no	—
137	C₄×M₁₆	—	118	1	no	—
138	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
139	C₄⋊C₁₆	—	118	2	no	—
140	#362	—	118	4	no	—
141	#361	—	118	4	no	—
142	#341	—	118	1	no	—
143	C₅₉	#13258	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	2	1	no	—
145	C₂²×D₄	—	2	1	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	2	2	no	—
148	C₂×Q₁₆	—	2	1	no	—
149	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
150	C₂×SD₁₆	—	2	4	no	—
151	C₂×SD₁₆	—	4	4	no	—
152	C₂×D₈	—	2	2	no	—
153	C₂×D₈	—	2	2	no	—
154	C₂×D₈	—	2	1	no	—
155	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
156	C₂×M₁₆	—	118	2	no	—
157	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
159	#124	—	2	4	no	—
160	#124	—	4	1	no	—
161	#124	—	4	1	no	—
162	C₂×C₂²⋊C₄	—	4	2	no	—
163	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
164	M₃₂	—	118	2	no	—
165	M₃₂	—	118	2	no	—
166	C₂×C₁₆	—	118	2	no	—
167	#108	—	59	4	no	—
168	#108	—	118	2	no	—
169	#97	—	236	1	no	—
170	C₄×C₈	—	236	1	no	—
171	C₄×C₈	C₂×Dic₅₉	1	2	yes	—
172	C₄×C₈	C₂²⋊D₅₉	1	2	yes	—
173	C₂⁴	—	4	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	4	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×D₄	—	2	2	no	—
179	C₂×D₄	—	4	2	no	—
180	C₂×D₄	—	4	1	no	—
181	C₂×D₄	—	4	2	no	—
182	C₂²×C₄	—	4	1	no	—
183	C₂²×C₄	#11745670	1	2	yes	—
184	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
185	Q₁₆	—	2	4	no	—
186	Q₁₆	—	4	1	no	—
187	Q₁₆	—	4	1	no	—
188	SD₁₆	—	4	8	no	—
189	D₈	—	2	4	no	—
190	D₈	—	4	1	no	—
191	D₈	—	4	1	no	—
192	M₁₆	—	118	4	no	—
193	M₁₆	—	236	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	236	2	no	—
196	C₂×C₈	C₂²⋊Dic₅₉	1	2	yes	—
197	C₂×C₈	D₄×D₅₉	1	2	yes	—
198	C₂×C₈	#11745687	1	2	yes	—
199	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
200	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
201	C₂²⋊C₄	—	4	4	no	—
202	C₂²⋊C₄	—	4	4	no	—
203	C₄²	#11745669	1	1	yes	characteristic
204	C₄²	#11745669	1	1	yes	characteristic
205	C₄²	C₂²⋊Dic₅₉	1	2	yes	—
206	C₁₆	—	236	2	no	—
207	C₂³	—	4	2	no	—
208	C₂³	—	8	4	no	—
209	C₂³	—	8	2	no	—
210	C₂³	C₂×#11745670	1	1	yes	characteristic
211	Q₈	—	4	2	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	8	2	no	—
214	D₄	—	4	2	no	—
215	D₄	—	4	2	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	8	2	no	—
220	C₂×C₄	#14273648	1	2	yes	—
221	C₂×C₄	#14273648	1	2	yes	—
222	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
223	C₂×C₄	#14273698	1	2	yes	—
224	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
225	C₂×C₄	#14273753	1	2	yes	—
226	C₈	—	2	2	no	—
227	C₈	—	236	4	no	—
228	C₈	D₄×Dic₅₉	1	2	yes	—
229	C₈	#14273714	1	1	yes	characteristic
230	C₈	#14273723	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	8	2	no	—
233	C₂²	—	8	4	no	—
234	C₂²	—	16	4	no	—
235	C₂²	C₂×#14273648	1	1	yes	characteristic
236	C₂²	#16837599	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	8	2	no	—
240	C₄	#16837305	1	1	yes	characteristic
241	C₄	#16837407	1	1	yes	characteristic
242	C₄	#16837594	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	16	2	no	—
245	C₂	#21425024	1	1	yes	characteristic
246	C₂	#21425845	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21425852

C₂

yes

maximal, characteristic, complemented

C₂×#16837218

C₂

yes

maximal, complemented

C₂×#16837215

C₂

yes

maximal

C₄×#14273663

C₂

yes

maximal, characteristic, complemented

C₂×C₅₉×#495

C₂

yes

maximal, characteristic

C₂×#14273667

C₂²

yes

—

C₂×#14273663

C₂²

yes

—

C₄×#11745664

—

C₄⋊(C₅₉⋊C₁₆)

—

#16837218

—

#16837215

—

#16837167

—

C₂²×Q₁₆×C₅₉

C₂²

yes

characteristic

C₂²×SD₁₆×C₅₉

—

C₂²×D₈×C₅₉

C₂²

yes

characteristic

C₂×#124×C₅₉

—

C₅₉×#495

—

C₅₉×#495

C₄

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

—

—

—

C₂×C₅₉⋊C₁₆

—

#14273663

—

#14273663

D₄

yes

—

#14273638

—

C₄×C₅₉⋊C₈

—

C₂²×Q₈×C₅₉

—

C₂²×D₄×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

—

C₂×Q₁₆×C₅₉

C₂×C₄

yes

—

C₂×SD₁₆×C₅₉

—

C₂×SD₁₆×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

C₂×C₄

yes

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

C₂³

yes

characteristic

#124×C₅₉

—

#124×C₅₉

—

#124×C₅₉

—

C₂×C₂²⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

C₂⁴×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

SD₁₆

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

Q₁₆×C₅₉

—

SD₁₆×C₅₉

—

D₈×C₅₉

—

D₈×C₅₉

—

D₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

C₂²⋊C₄

yes

—

C₄²×C₅₉

D₈

yes

characteristic

C₄²×C₅₉

D₈

yes

characteristic

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

C₂×SD₁₆

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

100

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

101

C₂×C₄×C₅₉

AGL(1,ℤ/8)

yes

—

102

C₈×C₅₉

—

103

C₈×C₅₉

C₄×D₄

yes

—

104

C₈×C₅₉

#124

yes

characteristic

105

C₈×C₅₉

#127

yes

characteristic

106

C₅₉⋊C₈

—

107

#13258

—

maximal, Sylow

108

C₂²×C₅₉

—

109

C₂²×C₅₉

—

110

C₂²×C₅₉

—

111

C₂²×C₅₉

—

112

C₂²×C₅₉

C₂×#102

yes

characteristic

113

C₂²×C₅₉

#460

yes

—

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

#390

yes

characteristic

118

C₄×C₅₉

#418

yes

characteristic

119

C₄×C₅₉

#459

yes

—

120

C₂×#495

D₅₉

yes

characteristic

121

#2150

—

122

C₂×#362

—

123

C₂×#361

—

124

C₄×#108

—

125

C₂×C₅₉

—

126

C₂×C₅₉

—

127

C₂×C₅₉

#1982

yes

characteristic

128

C₂×C₅₉

#2148

yes

—

129

C₂²×Q₁₆

C₂×D₅₉

yes

characteristic

130

C₂²×SD₁₆

—

131

C₂²×D₈

C₂×D₅₉

yes

characteristic

132

C₂×#124

—

133

C₂×M₃₂

—

134

#495

—

135

#495

Dic₅₉

yes

—

136

C₂×#108

—

137

C₄×M₁₆

—

118

—

138

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

139

C₄⋊C₁₆

—

118

—

140

#362

—

118

—

141

#361

—

118

—

142

#341

—

118

—

143

C₅₉

#13258

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

C₂×Dic₅₉

yes

—

150

C₂×SD₁₆

—

151

C₂×SD₁₆

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

155

C₂×D₈

C₂×Dic₅₉

yes

—

156

C₂×M₁₆

—

118

—

157

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

158

C₂²×C₈

C₂²×D₅₉

yes

characteristic

159

#124

—

160

#124

—

161

#124

—

162

C₂×C₂²⋊C₄

—

163

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

164

M₃₂

—

118

—

165

M₃₂

—

118

—

166

C₂×C₁₆

—

118

—

167

#108

—

168

#108

—

118

—

169

#97

—

236

—

170

C₄×C₈

—

236

—

171

C₄×C₈

C₂×Dic₅₉

yes

—

172

C₄×C₈

C₂²⋊D₅₉

yes

—

173

C₂⁴

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

#11745670

yes

—

184

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

187

Q₁₆

—

188

SD₁₆

—

189

D₈

—

190

D₈

—

191

D₈

—

192

M₁₆

—

118

—

193

M₁₆

—

236

—

194

C₂×C₈

—

195

C₂×C₈

—

236

—

196

C₂×C₈

C₂²⋊Dic₅₉

yes

—

197

C₂×C₈

D₄×D₅₉

yes

—

198

C₂×C₈

#11745687

yes

—

199

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

200

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

201

C₂²⋊C₄

—

202

C₂²⋊C₄

—

203

C₄²

#11745669

yes

characteristic

204

C₄²

#11745669

yes

characteristic

205

C₄²

C₂²⋊Dic₅₉

yes

—

206

C₁₆

—

236

—

207

C₂³

—

208

C₂³

—

209

C₂³

—

210

C₂³

C₂×#11745670

yes

characteristic

211

Q₈

—

212

Q₈

—

213

Q₈

—

214

D₄

—

215

D₄

—

216

D₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

#14273648

yes

—

221

C₂×C₄

#14273648

yes

—

222

C₂×C₄

C₂×C₂²⋊Dic₅₉

yes

characteristic

223

C₂×C₄

#14273698

yes

—

224

C₂×C₄

C₂×#11745669

yes

characteristic

225

C₂×C₄

#14273753

yes

—

226

C₈

—

227

C₈

—

236

—

228

C₈

D₄×Dic₅₉

yes

—

229

C₈

#14273714

yes

characteristic

230

C₈

#14273723

yes

characteristic

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

—

235

C₂²

C₂×#14273648

yes

characteristic

236

C₂²

#16837599

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

#16837305

yes

characteristic

241

C₄

#16837407

yes

characteristic

242

C₄

#16837594

yes

—

243

C₂

—

244

C₂

—

245

C₂

#21425024

yes

characteristic

246

C₂

#21425845

yes

—

	subgroup	G/H
center	C₂²	C₂×#14273648
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₂×C₅₉×#495	C₂
socle	C₂²×C₅₉	C₂×#102
prime radical	C₂²×D₈×C₅₉	C₂²
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂×#495	D₅₉
hypocenter	C₅₉	#13258
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

subgroup

G/H

center

C₂²

C₂×#14273648

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₂×C₅₉×#495

C₂

socle

C₂²×C₅₉

C₂×#102

prime radical

C₂²×D₈×C₅₉

C₂²

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#495

N	H ≅ G/N	type
1. #21425852	C₂	semidirect
2. C₂×#16837218	C₂	semidirect
4. C₄×#14273663	C₂	semidirect
143. C₅₉	#13258	semidirect

H ≅ G/N

type

1. #21425852

C₂

semidirect

2. C₂×#16837218

C₂

semidirect

4. C₄×#14273663

C₂

semidirect

143. C₅₉

#13258

semidirect

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

subgroup	index
#21425852	2
C₂×#16837218	2
C₂×#16837215	2
C₄×#14273663	2
C₂×C₅₉×#495	2
#13258	59

subgroup

index

C₂×C₅₉×#495

Subgroups — #28507183

Conjugacy classes of subgroups

Complements

Maximal subgroups