Group #21436745 — subgroups

Subgroups — #21436745

Order 7552.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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	#16838125	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837759	C₂	1	2	yes	maximal, complemented
3	#16837754	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837706	C₂	1	2	yes	maximal, complemented
5	#16837689	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837617	C₂	1	2	yes	maximal
7	#16837607	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11745670	C₂	1	2	yes	maximal, complemented
10	C₄×#11745669	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11745670	C₂²	1	2	yes	—
13	C₂×#11745669	C₂²	1	1	yes	characteristic
14	#14273727	C₂²	1	1	yes	characteristic
15	#14273722	—	2	2	no	—
16	#14273715	C₂²	1	2	yes	—
17	#14273703	—	2	1	no	—
18	C₄×Dic₁₁₈	C₂²	1	2	yes	—
19	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
20	#14273685	—	2	1	no	—
21	#14273660	C₂²	1	1	yes	characteristic
22	#14273658	C₂²	1	2	yes	—
23	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
25	#14273650	C₂²	1	2	yes	—
26	#14273650	C₂²	1	2	yes	—
27	#14273650	C₂²	1	2	yes	—
28	#14273648	C₂²	1	1	yes	characteristic
29	#14273647	C₂²	1	2	yes	—
30	#14273647	C₂²	1	1	yes	characteristic
31	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
34	#125×C₅₉	C₂²	1	2	yes	—
35	C₂²⋊Q₈×C₅₉	—	2	1	no	—
36	C₂²⋊Q₈×C₅₉	—	2	2	no	—
37	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₅₉	C₂²	1	2	yes	—
40	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
41	C₂×Q₈×C₅₉	—	2	1	no	—
42	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
43	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₅₉	—	2	1	no	—
45	C₂²×C₄×C₅₉	—	2	2	no	—
46	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
47	C₂×C₄×D₅₉	—	2	1	no	—
48	C₂×Dic₁₁₈	C₂³	1	2	yes	—
49	C₄⋊C₄×C₅₉	—	2	2	no	—
50	C₄⋊C₄×C₅₉	—	2	1	no	—
51	C₄⋊C₄×C₅₉	—	2	2	no	—
52	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
54	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
56	C₂²⋊C₄×C₅₉	—	2	1	no	—
57	C₂²⋊C₄×C₅₉	—	2	2	no	—
58	C₄²×C₅₉	C₂³	1	2	yes	—
59	C₄²×C₅₉	C₂³	1	1	yes	characteristic
60	#11745670	—	2	4	no	—
61	#11745669	—	2	2	no	—
62	(C₂×D₅₉)⋊C₄	—	2	2	no	—
63	(C₂×D₅₉)⋊C₄	—	2	1	no	—
64	(C₂×D₅₉)⋊C₄	—	2	2	no	—
65	C₄⋊Dic₅₉	—	2	1	no	—
66	C₄⋊Dic₅₉	—	2	1	no	—
67	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
68	Dic₅₉⋊C₄	—	2	2	no	—
69	C₄×Dic₅₉	—	2	2	no	—
70	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
72	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
73	C₂³×C₅₉	—	2	1	no	—
74	C₂²×D₅₉	—	2	1	no	—
75	Q₈×C₅₉	—	2	2	no	—
76	Q₈×C₅₉	—	8	1	no	—
77	D₄×C₅₉	—	2	1	no	—
78	D₄×C₅₉	#41	1	2	yes	—
79	C₂×C₄×C₅₉	—	2	1	no	—
80	C₂×C₄×C₅₉	—	2	2	no	—
81	C₂×C₄×C₅₉	—	4	2	no	—
82	C₂×C₄×C₅₉	—	8	2	no	—
83	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
84	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₅₉	—	2	1	no	—
89	C₂×Dic₅₉	—	2	2	no	—
90	D₂₃₆	—	2	1	no	—
91	D₂₃₆	—	2	1	no	—
92	C₄×D₅₉	—	4	2	no	—
93	Dic₁₁₈	—	2	2	no	—
94	Dic₁₁₈	—	2	2	no	—
95	C₅₉⋊C₈	—	2	1	no	—
96	C₅₉⋊C₈	—	2	2	no	—
97	C₅₉⋊C₈	—	2	1	no	—
98	C₂²×C₅₉	—	2	2	no	—
99	C₂²×C₅₉	—	4	1	no	—
100	C₂²×C₅₉	—	4	1	no	—
101	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₅₉	—	4	1	no	—
103	C₂×D₅₉	—	4	1	no	—
104	C₂×D₅₉	—	4	1	no	—
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	2	2	no	—
107	C₄×C₅₉	—	2	1	no	—
108	C₄×C₅₉	—	4	1	no	—
109	C₄×C₅₉	—	4	2	no	—
110	C₄×C₅₉	#135	1	2	yes	—
111	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
112	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
113	Dic₅₉	—	4	2	no	—
114	Dic₅₉	—	4	1	no	—
115	#3360	—	59	1	no	maximal, Sylow
116	C₂×C₅₉	—	4	2	no	—
117	C₂×C₅₉	#548	1	1	yes	characteristic
118	C₂×C₅₉	C₂×#135	1	1	yes	characteristic
119	C₂×C₅₉	#577	1	1	yes	characteristic
120	D₅₉	—	8	1	no	—
121	#556	—	59	1	no	—
122	#554	D₅₉	1	1	yes	characteristic, complemented
123	#488	—	59	2	no	—
124	#487	—	59	1	no	—
125	#479	—	59	2	no	—
126	#476	—	59	1	no	—
127	#463	—	59	2	no	—
128	#461	—	59	1	no	—
129	C₈×Q₈	—	59	1	no	—
130	C₄×SD₁₆	—	59	2	no	—
131	C₄×D₈	—	59	1	no	—
132	C₅₉	#3360	1	1	yes	characteristic, complemented, Sylow
133	C₂×SD₁₆	—	59	2	no	—
134	C₂×D₈	—	59	1	no	—
135	C₄⋊Q₈	—	59	1	no	—
136	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
137	#126	—	118	2	no	—
138	#125	C₂×D₅₉	1	2	yes	—
139	#124	—	59	2	no	—
140	C₂²⋊Q₈	—	2	1	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₂²⋊Q₈	—	118	1	no	—
143	C₄×Q₈	—	59	2	no	—
144	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
145	C₄×D₄	—	59	1	no	—
146	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
147	C₄×D₄	C₂×D₅₉	1	2	yes	—
148	#117	—	118	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	#107	—	59	1	no	—
151	#106	—	59	2	no	—
152	C₄⋊C₈	—	59	1	no	—
153	C₄⋊C₈	—	59	2	no	—
154	#103	—	59	2	no	—
155	#103	—	59	2	no	—
156	#103	—	59	2	no	—
157	#102	—	59	1	no	—
158	#102	—	59	1	no	—
159	#102	—	59	2	no	—
160	C₄×C₈	—	59	1	no	—
161	C₄×C₈	—	59	2	no	—
162	C₂×Q₈	—	2	1	no	—
163	C₂×Q₈	—	59	2	no	—
164	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
165	C₂×D₄	—	59	1	no	—
166	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
167	C₂²×C₄	—	2	1	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	118	1	no	—
170	SD₁₆	—	118	4	no	—
171	D₈	—	118	2	no	—
172	C₂×C₈	—	59	1	no	—
173	C₂×C₈	—	59	2	no	—
174	C₂×C₈	—	59	1	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	1	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	59	1	no	—
179	C₄⋊C₄	—	118	1	no	—
180	C₄⋊C₄	—	118	2	no	—
181	C₄⋊C₄	—	118	1	no	—
182	C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
183	C₄⋊C₄	C₂²⋊D₅₉	1	2	yes	—
184	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
185	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
186	C₂²⋊C₄	—	2	1	no	—
187	C₂²⋊C₄	—	2	2	no	—
188	C₂²⋊C₄	—	118	2	no	—
189	C₂²⋊C₄	—	118	1	no	—
190	C₂²⋊C₄	—	118	2	no	—
191	C₄²	—	118	2	no	—
192	C₄²	C₂²×D₅₉	1	1	yes	characteristic
193	C₄²	C₂²×D₅₉	1	2	yes	—
194	C₂³	—	2	1	no	—
195	C₂³	—	118	1	no	—
196	Q₈	—	2	2	no	—
197	Q₈	—	8	1	no	—
198	Q₈	—	118	2	no	—
199	Q₈	—	118	2	no	—
200	D₄	—	2	1	no	—
201	D₄	—	118	1	no	—
202	D₄	—	118	1	no	—
203	D₄	#11745689	1	2	yes	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	8	2	no	—
208	C₂×C₄	—	118	1	no	—
209	C₂×C₄	—	118	2	no	—
210	C₂×C₄	—	236	2	no	—
211	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
212	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
213	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
215	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
216	C₈	—	118	1	no	—
217	C₈	—	118	2	no	—
218	C₈	—	118	1	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	4	1	no	—
221	C₂²	—	4	1	no	—
222	C₂²	—	236	1	no	—
223	C₂²	—	236	1	no	—
224	C₂²	—	236	1	no	—
225	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	2	no	—
228	C₄	—	2	1	no	—
229	C₄	—	4	1	no	—
230	C₄	—	4	2	no	—
231	C₄	—	236	1	no	—
232	C₄	—	236	2	no	—
233	C₄	#14273747	1	2	yes	—
234	C₄	C₂×#11745689	1	1	yes	characteristic
235	C₄	#14273775	1	1	yes	characteristic
236	C₂	—	4	2	no	—
237	C₂	—	472	1	no	—
238	C₂	#16838063	1	1	yes	characteristic
239	C₂	C₂×#14273747	1	1	yes	characteristic
240	C₂	#16838213	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838125

C₂

yes

maximal, characteristic, complemented

#16837759

C₂

yes

maximal, complemented

#16837754

C₂

yes

maximal, characteristic, complemented

#16837706

C₂

yes

maximal, complemented

#16837689

C₂

yes

maximal, characteristic, complemented

#16837617

C₂

yes

maximal

#16837607

C₂

yes

maximal, characteristic, complemented

Q₈×C₅₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11745670

C₂

yes

maximal, complemented

C₄×#11745669

C₂

yes

maximal, characteristic

C₅₉×#554

C₂

yes

maximal, characteristic, complemented

C₂×#11745670

C₂²

yes

—

C₂×#11745669

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273722

—

#14273715

C₂²

yes

—

#14273703

—

C₄×Dic₁₁₈

C₂²

yes

—

C₄×D₂₃₆

C₂²

yes

characteristic

#14273685

—

#14273660

C₂²

yes

characteristic

#14273658

C₂²

yes

—

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273650

C₂²

yes

—

#14273650

C₂²

yes

—

#14273650

C₂²

yes

—

#14273648

C₂²

yes

characteristic

#14273647

C₂²

yes

—

#14273647

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

#125×C₅₉

C₂²

yes

—

C₂²⋊Q₈×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

C₂²

yes

—

C₂×C₄⋊C₄×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×D₄×C₅₉

C₂³

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

—

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

C₂³

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄⋊C₄×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₂³

yes

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

C₂³

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

#11745670

—

#11745669

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂³×C₅₉

—

C₂²×D₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

#41

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

—

C₄×D₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

100

C₂²×C₅₉

—

101

C₂²×C₅₉

C₂²×D₄

yes

characteristic

102

C₂×D₅₉

—

103

C₂×D₅₉

—

104

C₂×D₅₉

—

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

#135

yes

—

111

C₄×C₅₉

C₂×#41

yes

characteristic

112

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

113

Dic₅₉

—

114

Dic₅₉

—

115

#3360

—

maximal, Sylow

116

C₂×C₅₉

—

117

C₂×C₅₉

#548

yes

characteristic

118

C₂×C₅₉

C₂×#135

yes

characteristic

119

C₂×C₅₉

#577

yes

characteristic

120

D₅₉

—

121

#556

—

122

#554

D₅₉

yes

characteristic, complemented

123

#488

—

124

#487

—

125

#479

—

126

#476

—

127

#463

—

128

#461

—

129

C₈×Q₈

—

130

C₄×SD₁₆

—

131

C₄×D₈

—

132

C₅₉

#3360

yes

characteristic, complemented, Sylow

133

C₂×SD₁₆

—

134

C₂×D₈

—

135

C₄⋊Q₈

—

136

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

137

#126

—

118

—

138

#125

C₂×D₅₉

yes

—

139

#124

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₂²⋊Q₈

—

118

—

143

C₄×Q₈

—

144

C₄×Q₈

C₂×D₅₉

yes

characteristic

145

C₄×D₄

—

146

C₄×D₄

C₂×D₅₉

yes

characteristic

147

C₄×D₄

C₂×D₅₉

yes

—

148

#117

—

118

—

149

C₂×C₄⋊C₄

—

150

#107

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

#102

—

158

#102

—

159

#102

—

160

C₄×C₈

—

161

C₄×C₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

C₂²⋊D₅₉

yes

characteristic

165

C₂×D₄

—

166

C₂×D₄

C₂²×D₅₉

yes

characteristic

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

118

—

170

SD₁₆

—

118

—

171

D₈

—

118

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

118

—

180

C₄⋊C₄

—

118

—

181

C₄⋊C₄

—

118

—

182

C₄⋊C₄

C₂²⋊D₅₉

yes

characteristic

183

C₄⋊C₄

C₂²⋊D₅₉

yes

—

184

C₄⋊C₄

C₂²×D₅₉

yes

—

185

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

188

C₂²⋊C₄

—

118

—

189

C₂²⋊C₄

—

118

—

190

C₂²⋊C₄

—

118

—

191

C₄²

—

118

—

192

C₄²

C₂²×D₅₉

yes

characteristic

193

C₄²

C₂²×D₅₉

yes

—

194

C₂³

—

195

C₂³

—

118

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

118

—

199

Q₈

—

118

—

200

D₄

—

201

D₄

—

118

—

202

D₄

—

118

—

203

D₄

#11745689

yes

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

118

—

209

C₂×C₄

—

118

—

210

C₂×C₄

—

236

—

211

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

212

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

213

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

214

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

215

C₂×C₄

C₂³×D₅₉

yes

characteristic

216

C₈

—

118

—

217

C₈

—

118

—

218

C₈

—

118

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

—

236

—

223

C₂²

—

236

—

224

C₂²

—

236

—

225

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

236

—

232

C₄

—

236

—

233

C₄

#14273747

yes

—

234

C₄

C₂×#11745689

yes

characteristic

235

C₄

#14273775

yes

characteristic

236

C₂

—

237

C₂

—

472

—

238

C₂

#16838063

yes

characteristic

239

C₂

C₂×#14273747

yes

characteristic

240

C₂

#16838213

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#554	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#554	D₅₉
hypocenter	C₅₉	#3360
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#554

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #554

N	H ≅ G/N	type
1. #16838125	C₂	semidirect
2. #16837759	C₂	semidirect
3. #16837754	C₂	semidirect
4. #16837706	C₂	semidirect
5. #16837689	C₂	semidirect
7. #16837607	C₂	semidirect
8. Q₈×C₅₉⋊C₈	C₂	semidirect
9. C₄×#11745670	C₂	semidirect
11. C₅₉×#554	C₂	semidirect
122. #554	D₅₉	semidirect
132. C₅₉	#3360	semidirect

H ≅ G/N

type

1. #16838125

C₂

semidirect

2. #16837759

C₂

semidirect

3. #16837754

C₂

semidirect

4. #16837706

C₂

semidirect

5. #16837689

C₂

semidirect

7. #16837607

C₂

semidirect

8. Q₈×C₅₉⋊C₈

C₂

semidirect

9. C₄×#11745670

C₂

semidirect

11. C₅₉×#554

C₂

semidirect

122. #554

D₅₉

semidirect

132. C₅₉

#3360

semidirect

Subgroups — #21436745

Conjugacy classes of subgroups

Complements