Group #28487882 — subgroups

Subgroups — #28487882

Order 15104.

400 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 107 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	#21434682	C₂	1	1	yes	maximal, characteristic
2	#21422690	C₂	1	2	yes	maximal
3	#21422518	C₂	1	2	yes	maximal
4	C₈×#11745664	C₂	1	1	yes	maximal, characteristic
5	C₄×#108×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#16837959	C₂²	1	2	yes	—
7	#16837807	C₄	1	1	yes	characteristic
8	#16837782	C₄	1	1	yes	characteristic
9	#16837753	C₄	1	2	yes	—
10	#16837643	—	2	1	no	—
11	#16837643	—	2	1	no	—
12	C₄×Dic₂₃₆	—	2	1	no	—
13	C₄×Dic₂₃₆	—	2	1	no	—
14	#16837455	C₂²	1	1	yes	characteristic
15	C₄×#11745664	C₂²	1	1	yes	characteristic
16	#16837143	—	2	4	no	—
17	#16837134	—	2	4	no	—
18	#16837124	—	2	1	no	—
19	C₈×C₅₉⋊C₈	—	2	1	no	—
20	C₂×#108×C₅₉	—	2	1	no	—
21	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#341	—	2	1	no	—
24	C₂×Dic₂₃₆	—	2	1	no	—
25	C₂×Dic₂₃₆	—	2	1	no	—
26	C₂×#11745664	—	2	1	no	—
27	#14273727	C₂×C₄	1	2	yes	—
28	#14273727	C₂×C₄	1	2	yes	—
29	#14273719	—	2	2	no	—
30	#14273706	—	2	2	no	—
31	#14273706	—	2	2	no	—
32	C₄×Dic₁₁₈	—	2	2	no	—
33	C₄×Dic₁₁₈	—	2	2	no	—
34	#14273686	—	2	2	no	—
35	#14273661	—	2	1	no	—
36	#14273661	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
38	#14273652	—	2	2	no	—
39	#14273652	—	2	2	no	—
40	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
41	#14273638	D₄	1	2	yes	—
42	C₄×C₅₉⋊C₈	—	2	1	no	—
43	C₄×C₅₉⋊C₈	—	2	1	no	—
44	C₂×M₁₆×C₅₉	—	2	2	no	—
45	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
48	#108×C₅₉	—	2	4	no	—
49	#97×C₅₉	—	2	2	no	—
50	C₄×C₈×C₅₉	—	2	2	no	—
51	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
54	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
55	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
57	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
58	C₂×Dic₁₁₈	—	2	2	no	—
59	C₂×Dic₁₁₈	—	2	2	no	—
60	M₁₆×C₅₉	—	2	4	no	—
61	M₁₆×C₅₉	—	4	2	no	—
62	C₂×C₈×C₅₉	—	2	2	no	—
63	C₂×C₈×C₅₉	—	4	1	no	—
64	C₂×C₈×C₅₉	—	4	2	no	—
65	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
73	C₂²⋊Dic₅₉	—	4	2	no	—
74	C₄⋊Dic₅₉	—	2	2	no	—
75	C₄⋊Dic₅₉	—	2	2	no	—
76	C₄⋊Dic₅₉	—	2	2	no	—
77	C₄⋊Dic₅₉	—	2	2	no	—
78	Dic₅₉⋊C₄	—	4	2	no	—
79	Dic₅₉⋊C₄	—	4	2	no	—
80	C₄×Dic₅₉	—	4	2	no	—
81	#11745664	—	2	4	no	—
82	C₂×C₅₉⋊C₈	—	2	2	no	—
83	C₂×C₅₉⋊C₈	—	2	2	no	—
84	Dic₂₃₆	—	4	2	no	—
85	Dic₂₃₆	—	4	2	no	—
86	C₂³×C₅₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₅₉	—	2	1	no	—
88	C₂×C₄×C₅₉	—	2	1	no	—
89	C₂×C₄×C₅₉	—	2	2	no	—
90	C₂×C₄×C₅₉	—	2	2	no	—
91	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
95	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
96	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
97	C₂×Dic₅₉	—	4	2	no	—
98	C₂×Dic₅₉	—	4	2	no	—
99	Dic₁₁₈	—	4	2	no	—
100	Dic₁₁₈	—	4	2	no	—
101	Dic₁₁₈	—	4	4	no	—
102	C₈×C₅₉	—	2	1	no	—
103	C₈×C₅₉	—	2	1	no	—
104	C₈×C₅₉	—	2	1	no	—
105	C₈×C₅₉	—	4	4	no	—
106	C₈×C₅₉	#104	1	2	yes	—
107	C₅₉⋊C₈	—	2	4	no	—
108	C₅₉⋊C₈	—	4	2	no	—
109	#9725	—	59	1	no	maximal, Sylow
110	C₂²×C₅₉	—	2	1	no	—
111	C₂²×C₅₉	—	2	1	no	—
112	C₂²×C₅₉	—	2	1	no	—
113	C₂²×C₅₉	#390	1	1	yes	characteristic
114	C₄×C₅₉	—	2	1	no	—
115	C₄×C₅₉	—	2	1	no	—
116	C₄×C₅₉	—	2	1	no	—
117	C₄×C₅₉	C₂×#104	1	1	yes	characteristic
118	C₄×C₅₉	#421	1	1	yes	characteristic
119	C₄×C₅₉	#443	1	2	yes	—
120	C₄×C₅₉	#473	1	2	yes	—
121	Dic₅₉	—	8	2	no	—
122	Dic₅₉	—	8	2	no	—
123	#3170	—	59	1	no	—
124	C₄×#108	D₅₉	1	1	yes	characteristic
125	#1526	—	59	2	no	—
126	#1485	—	59	2	no	—
127	C₈×M₁₆	—	59	1	no	—
128	C₂×C₅₉	—	4	1	no	—
129	C₂×C₅₉	#1974	1	1	yes	characteristic
130	C₂×C₅₉	#1979	1	1	yes	characteristic
131	C₂×C₅₉	#1980	1	1	yes	characteristic
132	#533	—	59	2	no	—
133	#500	—	59	1	no	—
134	#494	—	59	1	no	—
135	#487	—	59	2	no	—
136	#467	—	118	1	no	—
137	#467	—	118	1	no	—
138	C₄×Q₁₆	—	118	1	no	—
139	C₄×Q₁₆	—	118	1	no	—
140	#431	—	59	1	no	—
141	C₂×#108	—	2	1	no	—
142	C₄×M₁₆	—	59	1	no	—
143	C₄×M₁₆	C₂×D₅₉	1	2	yes	—
144	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
145	#341	—	2	1	no	—
146	#330	—	118	4	no	—
147	Q₈⋊C₈	—	118	4	no	—
148	#322	—	118	1	no	—
149	C₈²	—	118	1	no	—
150	C₅₉	#9725	1	1	yes	characteristic, complemented, Sylow
151	C₂×Q₁₆	—	118	1	no	—
152	C₂×Q₁₆	—	118	1	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	118	1	no	—
155	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
156	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
157	C₄⋊Q₈	—	59	2	no	—
158	C₄⋊Q₈	—	59	2	no	—
159	#125	—	118	2	no	—
160	C₂²⋊Q₈	—	118	2	no	—
161	C₂²⋊Q₈	—	118	2	no	—
162	C₄×Q₈	—	118	2	no	—
163	C₄×Q₈	—	118	2	no	—
164	#117	—	118	2	no	—
165	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
166	#108	—	2	4	no	—
167	#107	—	118	1	no	—
168	#107	—	118	1	no	—
169	C₄⋊C₈	—	59	2	no	—
170	#103	—	118	2	no	—
171	#103	—	118	2	no	—
172	C₂²⋊C₈	—	118	1	no	—
173	#97	—	2	2	no	—
174	#97	—	59	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₄×C₈	—	118	1	no	—
177	C₄×C₈	—	118	1	no	—
178	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
179	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
180	C₄×C₈	D₂₃₆	1	1	yes	characteristic
181	C₄×C₈	D₂₃₆	1	1	yes	characteristic
182	C₂×Q₈	—	118	2	no	—
183	C₂×Q₈	—	118	2	no	—
184	C₂²×C₄	#11745689	1	1	yes	characteristic
185	C₂²×C₄	#11745689	1	1	yes	characteristic
186	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
187	Q₁₆	—	236	2	no	—
188	Q₁₆	—	236	2	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	—	4	2	no	—
191	M₁₆	—	118	4	no	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	2	no	—
195	C₂×C₈	—	118	2	no	—
196	C₂×C₈	—	118	2	no	—
197	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
198	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
199	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
201	C₄⋊C₄	—	118	2	no	—
202	C₄⋊C₄	—	118	2	no	—
203	C₄⋊C₄	—	118	2	no	—
204	C₄⋊C₄	—	118	2	no	—
205	C₄⋊C₄	—	236	2	no	—
206	C₄⋊C₄	—	236	2	no	—
207	C₂²⋊C₄	—	236	2	no	—
208	C₄²	—	236	2	no	—
209	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
210	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
211	C₄²	D₄×D₅₉	1	1	yes	characteristic
212	C₄²	D₄×D₅₉	1	1	yes	characteristic
213	C₂³	#14273716	1	1	yes	characteristic
214	Q₈	—	236	2	no	—
215	Q₈	—	236	2	no	—
216	Q₈	—	236	4	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	236	2	no	—
222	C₂×C₄	—	236	2	no	—
223	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
224	C₂×C₄	#14273689	1	1	yes	characteristic
225	C₂×C₄	#14273689	1	1	yes	characteristic
226	C₂×C₄	#14273702	1	1	yes	characteristic
227	C₂×C₄	#14273702	1	1	yes	characteristic
228	C₂×C₄	#14273723	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	2	1	no	—
232	C₈	—	4	4	no	—
233	C₈	—	118	4	no	—
234	C₈	—	236	2	no	—
235	C₈	#14273655	1	2	yes	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	2	1	no	—
239	C₂²	#16837303	1	1	yes	characteristic
240	C₄	—	2	1	no	—
241	C₄	—	2	1	no	—
242	C₄	—	2	1	no	—
243	C₄	—	472	2	no	—
244	C₄	—	472	2	no	—
245	C₄	C₂×#14273655	1	1	yes	characteristic
246	C₄	#16837420	1	1	yes	characteristic
247	C₄	#16837518	1	2	yes	—
248	C₄	#16837678	1	2	yes	—
249	C₂	—	4	1	no	—
250	C₂	#21424982	1	1	yes	characteristic
251	C₂	#21425009	1	1	yes	characteristic
252	C₂	#21425014	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21434682

C₂

yes

maximal, characteristic

#21422690

C₂

yes

maximal

#21422518

C₂

yes

maximal

C₈×#11745664

C₂

yes

maximal, characteristic

C₄×#108×C₅₉

C₂

yes

maximal, characteristic

#16837959

C₂²

yes

—

#16837807

C₄

yes

characteristic

#16837782

C₄

yes

characteristic

#16837753

C₄

yes

—

#16837643

—

#16837643

—

C₄×Dic₂₃₆

—

C₄×Dic₂₃₆

—

#16837455

C₂²

yes

characteristic

C₄×#11745664

C₂²

yes

—

—

—

C₈×C₅₉⋊C₈

—

C₂×#108×C₅₉

—

C₄×M₁₆×C₅₉

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#341

—

C₂×Dic₂₃₆

—

C₂×Dic₂₃₆

—

C₂×#11745664

—

#14273727

C₂×C₄

yes

—

#14273727

C₂×C₄

yes

—

#14273719

—

#14273706

—

#14273706

—

C₄×Dic₁₁₈

—

C₄×Dic₁₁₈

—

#14273686

—

#14273661

—

#14273661

—

C₄⋊(C₅₉⋊C₈)

D₄

yes

—

#14273652

—

#14273652

—

C₂²⋊(C₅₉⋊C₈)

—

#14273638

D₄

yes

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂×M₁₆×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#108×C₅₉

—

#97×C₅₉

—

C₄×C₈×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

C₂²×C₄×C₅₉

yes

C₂²×C₄×C₅₉

yes

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

M₁₆×C₅₉

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₅₉

C₂²⋊C₄

yes

characteristic

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

Dic₂₃₆

—

Dic₂₃₆

—

C₂³×C₅₉

#124

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×Dic₅₉

—

C₂×Dic₅₉

—

Dic₁₁₈

—

100

Dic₁₁₈

—

101

Dic₁₁₈

—

102

C₈×C₅₉

—

103

C₈×C₅₉

—

104

C₈×C₅₉

—

105

C₈×C₅₉

—

106

C₈×C₅₉

#104

yes

—

107

C₅₉⋊C₈

—

108

C₅₉⋊C₈

—

109

#9725

—

maximal, Sylow

110

C₂²×C₅₉

—

111

C₂²×C₅₉

—

112

C₂²×C₅₉

—

113

C₂²×C₅₉

#390

yes

characteristic

114

C₄×C₅₉

—

115

C₄×C₅₉

—

116

C₄×C₅₉

—

117

C₄×C₅₉

C₂×#104

yes

characteristic

118

C₄×C₅₉

#421

yes

characteristic

119

C₄×C₅₉

#443

yes

—

120

C₄×C₅₉

#473

yes

—

121

Dic₅₉

—

122

Dic₅₉

—

123

#3170

—

124

C₄×#108

D₅₉

yes

characteristic

125

#1526

—

126

#1485

—

127

C₈×M₁₆

—

128

C₂×C₅₉

—

129

C₂×C₅₉

#1974

yes

characteristic

130

C₂×C₅₉

#1979

yes

characteristic

131

C₂×C₅₉

#1980

yes

characteristic

132

#533

—

133

#500

—

134

#494

—

135

#487

—

136

#467

—

118

—

137

#467

—

118

—

138

C₄×Q₁₆

—

118

—

139

C₄×Q₁₆

—

118

—

140

#431

—

141

C₂×#108

—

142

C₄×M₁₆

—

143

C₄×M₁₆

C₂×D₅₉

yes

—

144

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

145

#341

—

146

#330

—

118

—

147

Q₈⋊C₈

—

118

—

148

#322

—

118

—

149

C₈²

—

118

—

150

C₅₉

#9725

yes

characteristic, complemented, Sylow

151

C₂×Q₁₆

—

118

—

152

C₂×Q₁₆

—

118

—

153

C₂×M₁₆

—

154

C₂×M₁₆

—

118

—

155

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

156

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

157

C₄⋊Q₈

—

158

C₄⋊Q₈

—

159

#125

—

118

—

160

C₂²⋊Q₈

—

118

—

161

C₂²⋊Q₈

—

118

—

162

C₄×Q₈

—

118

—

163

C₄×Q₈

—

118

—

164

#117

—

118

—

165

C₂×C₄²

C₂²×D₅₉

yes

characteristic

166

#108

—

167

#107

—

118

—

168

#107

—

118

—

169

C₄⋊C₈

—

170

#103

—

118

—

171

#103

—

118

—

172

C₂²⋊C₈

—

118

—

173

#97

—

174

#97

—

175

C₄×C₈

—

176

C₄×C₈

—

118

—

177

C₄×C₈

—

118

—

178

C₄×C₈

C₄×D₅₉

yes

characteristic

179

C₄×C₈

C₄×D₅₉

yes

characteristic

180

C₄×C₈

D₂₃₆

yes

characteristic

181

C₄×C₈

D₂₃₆

yes

characteristic

182

C₂×Q₈

—

118

—

183

C₂×Q₈

—

118

—

184

C₂²×C₄

#11745689

yes

characteristic

185

C₂²×C₄

#11745689

yes

characteristic

186

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

187

Q₁₆

—

236

—

188

Q₁₆

—

236

—

189

M₁₆

—

190

M₁₆

—

191

M₁₆

—

118

—

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

118

—

196

C₂×C₈

—

118

—

197

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

198

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

199

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

200

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

characteristic

201

C₄⋊C₄

—

118

—

202

C₄⋊C₄

—

118

—

203

C₄⋊C₄

—

118

—

204

C₄⋊C₄

—

118

—

205

C₄⋊C₄

—

236

—

206

C₄⋊C₄

—

236

—

207

C₂²⋊C₄

—

236

—

208

C₄²

—

236

—

209

C₄²

C₂×C₄×D₅₉

yes

characteristic

210

C₄²

C₂×D₂₃₆

yes

characteristic

211

C₄²

D₄×D₅₉

yes

characteristic

212

C₄²

D₄×D₅₉

yes

characteristic

213

C₂³

#14273716

yes

characteristic

214

Q₈

—

236

—

215

Q₈

—

236

—

216

Q₈

—

236

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

236

—

222

C₂×C₄

—

236

—

223

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

224

C₂×C₄

#14273689

yes

characteristic

225

C₂×C₄

#14273689

yes

characteristic

226

C₂×C₄

#14273702

yes

characteristic

227

C₂×C₄

#14273702

yes

characteristic

228

C₂×C₄

#14273723

yes

characteristic

229

C₈

—

230

C₈

—

231

C₈

—

232

C₈

—

233

C₈

—

118

—

234

C₈

—

236

—

235

C₈

#14273655

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

#16837303

yes

characteristic

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

472

—

244

C₄

—

472

—

245

C₄

C₂×#14273655

yes

characteristic

246

C₄

#16837420

yes

characteristic

247

C₄

#16837518

yes

—

248

C₄

#16837678

yes

—

249

C₂

—

250

C₂

#21424982

yes

characteristic

251

C₂

#21425009

yes

characteristic

252

C₂

#21425014

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14273702
commutator	C₄²×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₄×#108×C₅₉	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂³×C₅₉	#124
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₄×#108	D₅₉
hypocenter	C₅₉	#9725
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

subgroup

G/H

center

C₂×C₄

#14273702

commutator

C₄²×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₄×#108×C₅₉

C₂

C₂²×C₅₉

C₂³×C₅₉

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#108

N	H ≅ G/N	type
150. C₅₉	#9725	semidirect

H ≅ G/N

type

150. C₅₉

#9725

semidirect

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

subgroup	index
#21434682	2
#21422690	2
#21422518	2
C₈×#11745664	2
C₄×#108×C₅₉	2
#9725	59

subgroup

index

C₄×#108×C₅₉

Subgroups — #28487882

Conjugacy classes of subgroups

Complements

Maximal subgroups