Group #28486070 — subgroups

Subgroups — #28486070

Order 15104.

470 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 139 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	#21433177	C₂	1	1	yes	maximal, characteristic
2	#21424092	C₂	1	1	yes	maximal, characteristic
3	#21422781	C₂	1	2	yes	maximal
4	#21421999	C₂	1	2	yes	maximal
5	C₅₉×#2568	C₂	1	1	yes	maximal, characteristic
6	Q₈×C₅₉⋊C₈	—	2	4	no	—
7	#16837455	—	2	2	no	—
8	#16837455	C₂²	1	2	yes	—
9	#16837426	C₂²	1	2	yes	—
10	C₂×#14273646	—	2	1	no	—
11	#16837171	—	2	1	no	—
12	#16837148	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#400	C₄	1	4	yes	—
16	C₅₉×#391	—	2	1	no	—
17	C₅₉×#391	—	2	2	no	—
18	C₅₉×#382	—	2	1	no	—
19	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#11745664	—	2	2	no	—
21	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
22	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
23	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
24	C₄⋊(C₅₉⋊C₈)	D₄	1	4	yes	—
25	#14273646	—	4	2	no	—
26	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
27	C₄×C₅₉⋊C₈	—	2	4	no	—
28	C₄×C₅₉⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₅₉	—	2	1	no	—
30	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₅₉	—	2	2	no	—
32	C₄⋊Q₈×C₅₉	—	2	2	no	—
33	C₄×Q₈×C₅₉	—	2	2	no	—
34	C₄×Q₈×C₅₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₅₉	—	2	1	no	—
41	C₂×C₄²×C₅₉	D₄	1	2	yes	—
42	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
43	#95×C₅₉	—	2	4	no	—
44	#95×C₅₉	—	2	4	no	—
45	#95×C₅₉	C₂×C₄	1	2	yes	—
46	C₂×Q₈×C₅₉	—	2	2	no	—
47	C₂×Q₈×C₅₉	—	2	2	no	—
48	C₂×Q₈×C₅₉	—	4	4	no	—
49	C₂×Q₈×C₅₉	—	4	1	no	—
50	C₂×Q₈×C₅₉	—	4	1	no	—
51	C₂×Q₈×C₅₉	SD₁₆	1	2	yes	—
52	C₂×Q₈×C₅₉	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₅₉	—	2	2	no	—
54	C₂²×C₄×C₅₉	—	2	2	no	—
55	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₅₉	—	2	4	no	—
61	C₄⋊C₄×C₅₉	—	2	2	no	—
62	C₄⋊C₄×C₅₉	—	2	4	no	—
63	C₄⋊C₄×C₅₉	—	4	2	no	—
64	C₄⋊C₄×C₅₉	—	4	2	no	—
65	C₄²×C₅₉	—	2	2	no	—
66	C₄²×C₅₉	—	2	2	no	—
67	C₄²×C₅₉	—	4	2	no	—
68	C₄²×C₅₉	C₂×D₄	1	2	yes	—
69	C₄²×C₅₉	#41	1	2	yes	—
70	#11745664	—	4	2	no	—
71	#11745664	—	4	2	no	—
72	C₂×C₅₉⋊C₈	—	2	4	no	—
73	C₂×C₅₉⋊C₈	—	4	2	no	—
74	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₅₉	—	2	4	no	—
76	Q₈×C₅₉	—	2	4	no	—
77	Q₈×C₅₉	—	8	2	no	—
78	Q₈×C₅₉	—	8	2	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	—	2	2	no	—
81	C₂×C₄×C₅₉	—	2	2	no	—
82	C₂×C₄×C₅₉	—	2	2	no	—
83	C₂×C₄×C₅₉	—	4	1	no	—
84	C₂×C₄×C₅₉	—	4	2	no	—
85	C₂×C₄×C₅₉	—	4	2	no	—
86	C₂×C₄×C₅₉	—	4	2	no	—
87	C₂×C₄×C₅₉	—	4	4	no	—
88	C₂×C₄×C₅₉	—	4	2	no	—
89	C₂×C₄×C₅₉	—	4	2	no	—
90	C₂×C₄×C₅₉	#103	1	4	yes	—
91	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
93	C₂×C₄×C₅₉	#121	1	2	yes	—
94	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
95	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
97	C₂×C₄×C₅₉	#135	1	2	yes	—
98	C₅₉⋊C₈	—	4	4	no	—
99	C₅₉⋊C₈	—	8	2	no	—
100	#9396	—	59	1	no	maximal, Sylow
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	#386	1	1	yes	characteristic
104	C₂²×C₅₉	C₂×#103	1	1	yes	characteristic
105	C₂²×C₅₉	#416	1	1	yes	characteristic
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	—	2	4	no	—
108	C₄×C₅₉	—	2	2	no	—
109	C₄×C₅₉	—	4	2	no	—
110	C₄×C₅₉	—	8	2	no	—
111	C₄×C₅₉	—	8	2	no	—
112	C₄×C₅₉	#454	1	2	yes	—
113	C₄×C₅₉	#465	1	2	yes	—
114	C₄×C₅₉	#467	1	2	yes	—
115	#2982	—	59	1	no	—
116	#2568	D₅₉	1	1	yes	characteristic
117	#1801	—	59	1	no	—
118	#1549	—	59	2	no	—
119	#1303	—	59	2	no	—
120	C₂×C₅₉	—	2	1	no	—
121	C₂×C₅₉	—	2	1	no	—
122	C₂×C₅₉	#1888	1	1	yes	characteristic
123	C₂×C₅₉	#1892	1	1	yes	characteristic
124	C₂×C₅₉	#1915	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
126	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
127	C₈×Q₈	—	118	4	no	—
128	#431	—	59	2	no	—
129	#431	—	118	2	no	—
130	#423	—	59	2	no	—
131	C₂×#101	—	118	1	no	—
132	#400	Dic₅₉	1	4	yes	—
133	#391	—	2	1	no	—
134	#391	—	2	2	no	—
135	#382	—	2	1	no	—
136	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
137	#343	—	118	1	no	—
138	#332	—	118	4	no	—
139	C₅₉	#9396	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
142	C₂×M₁₆	—	118	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	C₂×Dic₅₉	1	2	yes	—
150	C₂×C₄⋊C₄	C₂×Dic₅₉	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	C₂²⋊D₅₉	1	2	yes	—
154	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
155	C₄⋊C₈	—	59	4	no	—
156	C₄⋊C₈	—	118	4	no	—
157	C₄⋊C₈	—	118	2	no	—
158	C₄⋊C₈	—	118	2	no	—
159	#101	—	236	2	no	—
160	C₂²⋊C₈	—	118	2	no	—
161	C₄×C₈	—	118	4	no	—
162	C₄×C₈	—	118	2	no	—
163	#95	—	2	4	no	—
164	#95	—	2	4	no	—
165	#95	C₂×Dic₅₉	1	2	yes	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	4	4	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×Q₈	#11745671	1	2	yes	—
172	C₂×Q₈	#11745672	1	2	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊Dic₅₉	1	2	yes	—
176	C₂²×C₄	C₂²⋊Dic₅₉	1	2	yes	—
177	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
180	M₁₆	—	236	2	no	—
181	M₁₆	—	236	2	no	—
182	C₂×C₈	—	118	4	no	—
183	C₂×C₈	—	236	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	4	2	no	—
192	C₄²	D₄×D₅₉	1	2	yes	—
193	C₄²	#11745687	1	2	yes	—
194	C₂³	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	8	2	no	—
198	Q₈	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	#14273651	1	4	yes	—
211	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
212	C₂×C₄	#14273695	1	1	yes	characteristic
213	C₂×C₄	#14273699	1	2	yes	—
214	C₂×C₄	#14273708	1	1	yes	characteristic
215	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
216	C₂×C₄	C₂×#11745672	1	1	yes	characteristic
217	C₂×C₄	#14273747	1	2	yes	—
218	C₈	—	472	2	no	—
219	C₈	—	236	4	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#16837282	1	1	yes	characteristic
223	C₂²	C₂×#14273651	1	1	yes	characteristic
224	C₂²	#16837398	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	4	no	—
228	C₄	—	4	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	8	2	no	—
231	C₄	#16837574	1	2	yes	—
232	C₄	#16837633	1	2	yes	—
233	C₄	#16837641	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#21424500	1	1	yes	characteristic
237	C₂	#21424520	1	1	yes	characteristic
238	C₂	#21424649	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21433177

C₂

yes

maximal, characteristic

#21424092

C₂

yes

maximal, characteristic

#21422781

C₂

yes

maximal

#21421999

C₂

yes

maximal

C₅₉×#2568

C₂

yes

maximal, characteristic

Q₈×C₅₉⋊C₈

—

#16837455

—

#16837455

C₂²

yes

—

#16837426

C₂²

yes

—

C₂×#14273646

—

#16837171

—

#16837148

—

C₂×C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₅₉×#400

C₄

yes

—

C₅₉×#391

—

C₅₉×#391

—

C₅₉×#382

—

C₄×C₄⋊C₄×C₅₉

C₂²

yes

characteristic

C₂×#11745664

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

#14273646

—

C₂²⋊(C₅₉⋊C₈)

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂²×Q₈×C₅₉

—

C₂²×Q₈×C₅₉

D₄

yes

characteristic

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₅₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

—

C₂×C₄²×C₅₉

D₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#95×C₅₉

—

#95×C₅₉

—

#95×C₅₉

C₂×C₄

yes

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

SD₁₆

yes

—

C₂×Q₈×C₅₉

Q₁₆

yes

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

—

C₄²×C₅₉

#41

yes

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#103

yes

—

C₂×C₄×C₅₉

C₄×D₄

yes

—

C₂×C₄×C₅₉

#120

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

#123

yes

characteristic

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₅₉

#135

yes

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

100

#9396

—

maximal, Sylow

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

#386

yes

characteristic

104

C₂²×C₅₉

C₂×#103

yes

characteristic

105

C₂²×C₅₉

#416

yes

characteristic

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

#454

yes

—

113

C₄×C₅₉

#465

yes

—

114

C₄×C₅₉

#467

yes

—

115

#2982

—

116

#2568

D₅₉

yes

characteristic

117

#1801

—

118

#1549

—

119

#1303

—

120

C₂×C₅₉

—

121

C₂×C₅₉

—

122

C₂×C₅₉

#1888

yes

characteristic

123

C₂×C₅₉

#1892

yes

characteristic

124

C₂×C₅₉

#1915

yes

characteristic

125

C₂×C₄⋊Q₈

C₂×D₅₉

yes

characteristic

126

C₂×C₄×Q₈

C₂×D₅₉

yes

characteristic

127

C₈×Q₈

—

118

—

128

#431

—

129

#431

—

118

—

130

#423

—

131

C₂×#101

—

118

—

132

#400

Dic₅₉

yes

—

133

#391

—

134

#391

—

135

#382

—

136

C₄×C₄⋊C₄

C₂×D₅₉

yes

characteristic

137

#343

—

118

—

138

#332

—

118

—

139

C₅₉

#9396

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂²×Q₈

C₂²⋊D₅₉

yes

characteristic

142

C₂×M₁₆

—

118

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×Dic₅₉

yes

—

150

C₂×C₄⋊C₄

C₂×Dic₅₉

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₅₉

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

C₂²⋊D₅₉

yes

—

154

C₂×C₄²

C₂²×D₅₉

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

118

—

157

C₄⋊C₈

—

118

—

158

C₄⋊C₈

—

118

—

159

#101

—

236

—

160

C₂²⋊C₈

—

118

—

161

C₄×C₈

—

118

—

162

C₄×C₈

—

118

—

163

#95

—

164

#95

—

165

#95

C₂×Dic₅₉

yes

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#11745671

yes

—

172

C₂×Q₈

#11745672

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊Dic₅₉

yes

—

176

C₂²×C₄

C₂²⋊Dic₅₉

yes

—

177

C₂²×C₄

C₂²×Dic₅₉

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

180

M₁₆

—

236

—

181

M₁₆

—

236

—

182

C₂×C₈

—

118

—

183

C₂×C₈

—

236

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₅₉

yes

—

193

C₄²

#11745687

yes

—

194

C₂³

C₂×C₂²⋊Dic₅₉

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14273651

yes

—

211

C₂×C₄

D₄×Dic₅₉

yes

—

212

C₂×C₄

#14273695

yes

characteristic

213

C₂×C₄

#14273699

yes

—

214

C₂×C₄

#14273708

yes

characteristic

215

C₂×C₄

C₂×#11745671

yes

characteristic

216

C₂×C₄

C₂×#11745672

yes

characteristic

217

C₂×C₄

#14273747

yes

—

218

C₈

—

472

—

219

C₈

—

236

—

220

C₂²

—

221

C₂²

—

222

C₂²

#16837282

yes

characteristic

223

C₂²

C₂×#14273651

yes

characteristic

224

C₂²

#16837398

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

#16837574

yes

—

232

C₄

#16837633

yes

—

233

C₄

#16837641

yes

—

234

C₂

—

235

C₂

—

236

C₂

#21424500

yes

characteristic

237

C₂

#21424520

yes

characteristic

238

C₂

#21424649

yes

characteristic

	subgroup	G/H
center	C₂²	#16837282
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#2568	C₂
socle	C₂²×C₅₉	#386
prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#2568	D₅₉
hypocenter	C₅₉	#9396
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

subgroup

G/H

center

C₂²

#16837282

commutator

C₂²×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#2568

C₂

socle

C₂²×C₅₉

#386

prime radical

C₂³×C₅₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

N	H ≅ G/N	type
139. C₅₉	#9396	semidirect

H ≅ G/N

type

139. C₅₉

#9396

semidirect

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

subgroup	index
#21433177	2
#21424092	2
#21422781	2
#21421999	2
C₅₉×#2568	2
#9396	59

subgroup

index

C₅₉×#2568

Subgroups — #28486070

Conjugacy classes of subgroups

Complements

Maximal subgroups