Group #21437080 — subgroups

Subgroups — #21437080

Order 7552.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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	#16837784	C₂	1	2	yes	maximal
3	#16837781	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837624	C₂	1	2	yes	maximal, complemented
5	#16837621	C₂	1	2	yes	maximal, complemented
6	#16837607	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837604	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11745672	C₂	1	2	yes	maximal, complemented
10	C₄×#11745669	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11745672	C₂²	1	2	yes	—
13	C₂×#11745672	C₂²	1	2	yes	—
14	C₂×#11745670	C₂²	1	2	yes	—
15	C₂×#11745671	C₂²	1	2	yes	—
16	C₂×#11745669	C₂²	1	1	yes	characteristic
17	#14273727	C₂²	1	1	yes	characteristic
18	#14273722	—	2	2	no	—
19	#14273715	C₂²	1	2	yes	—
20	#14273703	—	2	1	no	—
21	C₄×Dic₁₁₈	C₂²	1	2	yes	—
22	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
23	#14273685	—	2	1	no	—
24	#14273660	C₂²	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
27	#14273651	C₂²	1	2	yes	—
28	#14273650	C₂²	1	2	yes	—
29	#14273648	C₂²	1	1	yes	characteristic
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	#126×C₅₉	—	2	2	no	—
35	#124×C₅₉	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₅₉	—	2	1	no	—
37	C₄×Q₈×C₅₉	C₂²	1	2	yes	—
38	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
40	#117×C₅₉	—	2	1	no	—
41	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₅₉	C₂³	1	2	yes	—
43	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₅₉	—	2	1	no	—
45	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
46	C₂×C₄×D₅₉	—	2	1	no	—
47	C₂×Dic₁₁₈	C₂³	1	2	yes	—
48	C₄⋊C₄×C₅₉	—	2	1	no	—
49	C₄⋊C₄×C₅₉	—	2	2	no	—
50	C₄⋊C₄×C₅₉	—	2	1	no	—
51	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
52	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
53	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²⋊C₄×C₅₉	—	2	2	no	—
55	C₂²⋊C₄×C₅₉	—	2	1	no	—
56	C₂²⋊C₄×C₅₉	—	2	2	no	—
57	C₄²×C₅₉	—	2	2	no	—
58	C₄²×C₅₉	C₂³	1	1	yes	characteristic
59	C₄²×C₅₉	C₂³	1	2	yes	—
60	#11745672	—	2	4	no	—
61	#11745672	—	4	2	no	—
62	#11745671	—	4	2	no	—
63	#11745670	—	4	2	no	—
64	#11745669	—	2	2	no	—
65	(C₂×D₅₉)⋊C₄	—	2	2	no	—
66	(C₂×D₅₉)⋊C₄	—	2	1	no	—
67	(C₂×D₅₉)⋊C₄	—	2	2	no	—
68	C₄⋊Dic₅₉	—	2	1	no	—
69	C₄⋊Dic₅₉	—	2	1	no	—
70	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
71	Dic₅₉⋊C₄	—	2	2	no	—
72	C₄×Dic₅₉	—	2	2	no	—
73	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂³×C₅₉	—	2	1	no	—
77	C₂²×D₅₉	—	2	1	no	—
78	Q₈×C₅₉	—	2	2	no	—
79	Q₈×C₅₉	—	2	2	no	—
80	Q₈×C₅₉	—	2	2	no	—
81	D₄×C₅₉	—	2	1	no	—
82	D₄×C₅₉	—	2	1	no	—
83	C₂×C₄×C₅₉	—	2	1	no	—
84	C₂×C₄×C₅₉	—	2	2	no	—
85	C₂×C₄×C₅₉	—	4	2	no	—
86	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
87	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₅₉	—	2	1	no	—
92	C₂×Dic₅₉	—	2	2	no	—
93	D₂₃₆	—	2	1	no	—
94	D₂₃₆	—	2	1	no	—
95	C₄×D₅₉	—	4	2	no	—
96	Dic₁₁₈	—	2	2	no	—
97	Dic₁₁₈	—	2	2	no	—
98	C₅₉⋊C₈	—	2	2	no	—
99	C₅₉⋊C₈	—	2	1	no	—
100	C₅₉⋊C₈	#41	1	2	yes	—
101	C₂²×C₅₉	—	4	1	no	—
102	C₂²×C₅₉	—	4	1	no	—
103	C₂²×C₅₉	—	4	1	no	—
104	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₅₉	—	4	1	no	—
106	C₂×D₅₉	—	4	1	no	—
107	C₂×D₅₉	—	4	1	no	—
108	C₄×C₅₉	—	2	2	no	—
109	C₄×C₅₉	—	2	2	no	—
110	C₄×C₅₉	—	2	1	no	—
111	C₄×C₅₉	—	4	2	no	—
112	C₄×C₅₉	—	4	1	no	—
113	C₄×C₅₉	#135	1	2	yes	—
114	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
115	C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
116	Dic₅₉	—	4	2	no	—
117	Dic₅₉	—	4	1	no	—
118	#3393	—	59	1	no	maximal, Sylow
119	C₂×C₅₉	—	8	1	no	—
120	C₂×C₅₉	#550	1	1	yes	characteristic
121	C₂×C₅₉	C₂×#135	1	1	yes	characteristic
122	C₂×C₅₉	#578	1	1	yes	characteristic
123	D₅₉	—	8	1	no	—
124	#556	—	59	1	no	—
125	#556	D₅₉	1	1	yes	characteristic, complemented
126	#495	—	59	2	no	—
127	#494	—	59	1	no	—
128	#464	—	59	2	no	—
129	#464	—	59	2	no	—
130	#461	—	59	1	no	—
131	#461	—	59	1	no	—
132	C₈×Q₈	—	59	1	no	—
133	C₄×Q₁₆	—	59	2	no	—
134	C₄×D₈	—	59	1	no	—
135	C₅₉	#3393	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	59	2	no	—
137	C₂×Q₁₆	—	59	2	no	—
138	C₂×SD₁₆	—	59	2	no	—
139	C₂×SD₁₆	—	59	2	no	—
140	C₂×D₈	—	59	1	no	—
141	C₄⋊Q₈	—	59	1	no	—
142	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
143	#126	—	2	2	no	—
144	#126	—	118	2	no	—
145	#124	—	59	2	no	—
146	#124	C₂×D₅₉	1	2	yes	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₂²⋊Q₈	—	118	1	no	—
149	C₄×Q₈	—	59	2	no	—
150	C₄×Q₈	C₂×D₅₉	1	2	yes	—
151	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
152	C₄×D₄	—	59	1	no	—
153	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
154	#117	—	2	1	no	—
155	#117	—	118	1	no	—
156	#107	—	59	1	no	—
157	C₄⋊C₈	—	59	1	no	—
158	C₄⋊C₈	—	59	2	no	—
159	#103	—	59	2	no	—
160	#103	—	59	2	no	—
161	#102	—	59	1	no	—
162	#102	—	59	1	no	—
163	C₄×C₈	—	59	1	no	—
164	C₄×C₈	—	59	2	no	—
165	C₂×Q₈	—	59	2	no	—
166	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
167	C₂×Q₈	C₂²×D₅₉	1	2	yes	—
168	C₂×D₄	—	59	1	no	—
169	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	118	1	no	—
172	Q₁₆	—	118	4	no	—
173	Q₁₆	—	236	2	no	—
174	SD₁₆	—	236	2	no	—
175	SD₁₆	—	236	2	no	—
176	D₈	—	118	2	no	—
177	C₂×C₈	—	59	1	no	—
178	C₂×C₈	—	59	1	no	—
179	C₂×C₈	—	59	2	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	59	1	no	—
184	C₄⋊C₄	—	118	1	no	—
185	C₄⋊C₄	—	118	2	no	—
186	C₄⋊C₄	—	118	1	no	—
187	C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
188	C₄⋊C₄	C₂²⋊D₅₉	1	2	yes	—
189	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	1	no	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	118	2	no	—
194	C₂²⋊C₄	—	118	1	no	—
195	C₂²⋊C₄	—	118	2	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	118	2	no	—
198	C₄²	C₂²×D₅₉	1	1	yes	characteristic
199	C₄²	C₂²×D₅₉	1	2	yes	—
200	C₂³	—	2	1	no	—
201	C₂³	—	118	1	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	2	2	no	—
204	Q₈	—	2	2	no	—
205	Q₈	—	118	2	no	—
206	Q₈	—	118	2	no	—
207	D₄	—	2	1	no	—
208	D₄	—	2	1	no	—
209	D₄	—	118	1	no	—
210	D₄	—	118	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	118	1	no	—
215	C₂×C₄	—	118	2	no	—
216	C₂×C₄	—	236	2	no	—
217	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
220	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
221	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
222	C₈	—	59	2	no	—
223	C₈	—	118	2	no	—
224	C₈	—	118	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	236	1	no	—
229	C₂²	—	236	1	no	—
230	C₂²	—	236	1	no	—
231	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	2	no	—
237	C₄	—	236	1	no	—
238	C₄	—	236	2	no	—
239	C₄	#14273747	1	2	yes	—
240	C₄	#41×D₅₉	1	1	yes	characteristic
241	C₄	#14273773	1	1	yes	characteristic
242	C₂	—	8	1	no	—
243	C₂	—	472	1	no	—
244	C₂	#16838071	1	1	yes	characteristic
245	C₂	C₂×#14273747	1	1	yes	characteristic
246	C₂	#16838217	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838125

C₂

yes

maximal, characteristic, complemented

#16837784

C₂

yes

maximal

#16837781

C₂

yes

maximal, characteristic, complemented

#16837624

C₂

yes

maximal, complemented

#16837621

C₂

yes

maximal, complemented

#16837607

C₂

yes

maximal, characteristic, complemented

#16837604

C₂

yes

maximal, characteristic, complemented

Q₈×C₅₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11745672

C₂

yes

maximal, complemented

C₄×#11745669

C₂

yes

maximal, characteristic

C₅₉×#556

C₂

yes

maximal, characteristic, complemented

C₂×#11745672

C₂²

yes

—

C₂×#11745672

C₂²

yes

—

C₂×#11745670

C₂²

yes

—

C₂×#11745671

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

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273651

C₂²

yes

—

#14273650

C₂²

yes

—

#14273648

C₂²

yes

characteristic

#14273647

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

#126×C₅₉

—

#124×C₅₉

C₂²

yes

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

C₂²

yes

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄×D₄×C₅₉

C₂²

yes

characteristic

#117×C₅₉

—

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×Q₈×C₅₉

C₂³

yes

—

C₂×D₄×C₅₉

C₂³

yes

characteristic

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

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

—

—

—

—

—

—

(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

—

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×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

—

100

C₅₉⋊C₈

#41

yes

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

—

104

C₂²×C₅₉

C₂²×D₄

yes

characteristic

105

C₂×D₅₉

—

106

C₂×D₅₉

—

107

C₂×D₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

—

111

C₄×C₅₉

—

112

C₄×C₅₉

—

113

C₄×C₅₉

#135

yes

—

114

C₄×C₅₉

C₂×#41

yes

characteristic

115

C₄×C₅₉

H(5,𝔽₂)

yes

characteristic

116

Dic₅₉

—

117

Dic₅₉

—

118

#3393

—

maximal, Sylow

119

C₂×C₅₉

—

120

C₂×C₅₉

#550

yes

characteristic

121

C₂×C₅₉

C₂×#135

yes

characteristic

122

C₂×C₅₉

#578

yes

characteristic

123

D₅₉

—

124

#556

—

125

#556

D₅₉

yes

characteristic, complemented

126

#495

—

127

#494

—

128

#464

—

129

#464

—

130

#461

—

131

#461

—

132

C₈×Q₈

—

133

C₄×Q₁₆

—

134

C₄×D₈

—

135

C₅₉

#3393

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×D₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

143

#126

—

144

#126

—

118

—

145

#124

—

146

#124

C₂×D₅₉

yes

—

147

C₂²⋊Q₈

—

148

C₂²⋊Q₈

—

118

—

149

C₄×Q₈

—

150

C₄×Q₈

C₂×D₅₉

yes

—

151

C₄×Q₈

C₂×D₅₉

yes

characteristic

152

C₄×D₄

—

153

C₄×D₄

C₂×D₅₉

yes

characteristic

154

#117

—

155

#117

—

118

—

156

#107

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#103

—

160

#103

—

161

#102

—

162

#102

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₂×Q₈

—

166

C₂×Q₈

C₂²⋊D₅₉

yes

characteristic

167

C₂×Q₈

C₂²×D₅₉

yes

—

168

C₂×D₄

—

169

C₂×D₄

C₂²×D₅₉

yes

characteristic

170

C₂²×C₄

—

171

C₂²×C₄

—

118

—

172

Q₁₆

—

118

—

173

Q₁₆

—

236

—

174

SD₁₆

—

236

—

175

SD₁₆

—

236

—

176

D₈

—

118

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

118

—

185

C₄⋊C₄

—

118

—

186

C₄⋊C₄

—

118

—

187

C₄⋊C₄

C₂²⋊D₅₉

yes

characteristic

188

C₄⋊C₄

C₂²⋊D₅₉

yes

—

189

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

118

—

194

C₂²⋊C₄

—

118

—

195

C₂²⋊C₄

—

118

—

196

C₄²

—

197

C₄²

—

118

—

198

C₄²

C₂²×D₅₉

yes

characteristic

199

C₄²

C₂²×D₅₉

yes

—

200

C₂³

—

201

C₂³

—

118

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

118

—

206

Q₈

—

118

—

207

D₄

—

208

D₄

—

209

D₄

—

118

—

210

D₄

—

118

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

118

—

215

C₂×C₄

—

118

—

216

C₂×C₄

—

236

—

217

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

218

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

219

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

220

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

221

C₂×C₄

C₂³×D₅₉

yes

characteristic

222

C₈

—

223

C₈

—

118

—

224

C₈

—

118

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

236

—

229

C₂²

—

236

—

230

C₂²

—

236

—

231

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

236

—

238

C₄

—

236

—

239

C₄

#14273747

yes

—

240

C₄

#41×D₅₉

yes

characteristic

241

C₄

#14273773

yes

characteristic

242

C₂

—

243

C₂

—

472

—

244

C₂

#16838071

yes

characteristic

245

C₂

C₂×#14273747

yes

characteristic

246

C₂

#16838217

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#556	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#556	D₅₉
hypocenter	C₅₉	#3393
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#556

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #16838125	C₂	semidirect
3. #16837781	C₂	semidirect
4. #16837624	C₂	semidirect
5. #16837621	C₂	semidirect
6. #16837607	C₂	semidirect
7. #16837604	C₂	semidirect
8. Q₈×C₅₉⋊C₈	C₂	semidirect
9. C₄×#11745672	C₂	semidirect
11. C₅₉×#556	C₂	semidirect
125. #556	D₅₉	semidirect
135. C₅₉	#3393	semidirect

H ≅ G/N

type

1. #16838125

C₂

semidirect

3. #16837781

C₂

semidirect

4. #16837624

C₂

semidirect

5. #16837621

C₂

semidirect

6. #16837607

C₂

semidirect

7. #16837604

C₂

semidirect

8. Q₈×C₅₉⋊C₈

C₂

semidirect

9. C₄×#11745672

C₂

semidirect

11. C₅₉×#556

C₂

semidirect

125. #556

D₅₉

semidirect

135. C₅₉

#3393

semidirect

Subgroups — #21437080

Conjugacy classes of subgroups

Complements