Group #29574477 — subgroups

Subgroups — #29574477

Order 15616.

476 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 147 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	#21448909	C₂	1	1	yes	maximal, characteristic
2	#21446580	C₂	1	2	yes	maximal
3	C₂×#16839511	C₂	1	1	yes	maximal, characteristic
4	#21443659	C₂	1	2	yes	maximal
5	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519708	—	2	2	no	—
7	C₂×C₄⋊#92418	C₂²	1	2	yes	—
8	#16839669	—	2	2	no	—
9	#16839661	—	2	2	no	—
10	C₄⋊C₄×Dic₆₁	—	2	2	no	—
11	C₄×C₄⋊Dic₆₁	C₂²	1	2	yes	—
12	#16839524	—	2	2	no	—
13	#16839511	C₄	1	4	yes	complemented
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#103×C₆₁	—	2	2	no	—
16	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#384	C₂²	1	1	yes	characteristic
18	C₂²×#92418	—	2	2	no	—
19	C₂×C₄⋊Dic₆₁	—	2	2	no	—
20	C₂×C₄⋊Dic₆₁	D₄	1	2	yes	—
21	C₂×C₄⋊Dic₆₁	D₄	1	2	yes	—
22	C₂×C₄×Dic₆₁	—	2	2	no	—
23	C₂×C₄×Dic₆₁	—	2	2	no	—
24	#14519708	—	4	4	no	—
25	C₄⋊#92418	—	2	2	no	—
26	C₄⋊#92418	C₂×C₄	1	4	yes	—
27	#14519684	—	2	4	no	—
28	#14519684	—	2	2	no	—
29	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
30	C₂²×C₈×C₆₁	—	2	1	no	—
31	C₄⋊Q₈×C₆₁	—	2	2	no	—
32	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
33	C₄⋊Q₈×C₆₁	Q₈	1	2	yes	—
34	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
36	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
37	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
38	#103×C₆₁	—	4	4	no	—
39	C₄×C₈×C₆₁	—	2	2	no	—
40	C₂×Q₈×C₆₁	—	2	2	no	—
41	C₂×Q₈×C₆₁	—	4	2	no	—
42	C₂×Q₈×C₆₁	—	4	2	no	—
43	C₂×Q₈×C₆₁	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₆₁	—	2	2	no	—
45	C₂²×C₄×C₆₁	—	4	1	no	—
46	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
48	C₂²×Dic₆₁	—	2	2	no	—
49	C₂²×Dic₆₁	—	2	2	no	—
50	C₂×C₈×C₆₁	—	2	2	no	—
51	C₂×C₈×C₆₁	—	4	1	no	—
52	C₂×C₈×C₆₁	—	4	1	no	—
53	C₄⋊C₄×C₆₁	—	2	4	no	—
54	C₄⋊C₄×C₆₁	—	2	4	no	—
55	C₄⋊C₄×C₆₁	—	4	2	no	—
56	C₄⋊C₄×C₆₁	—	4	2	no	—
57	C₄⋊C₄×C₆₁	—	4	2	no	—
58	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₆₁	#41	1	2	yes	—
61	C₄⋊Dic₆₁	—	2	2	no	—
62	C₄⋊Dic₆₁	—	2	2	no	—
63	C₄⋊Dic₆₁	—	2	2	no	—
64	C₄⋊Dic₆₁	—	8	2	no	—
65	C₄⋊Dic₆₁	SD₁₆	1	4	yes	—
66	C₄×Dic₆₁	—	4	2	no	—
67	C₄×Dic₆₁	—	4	2	no	—
68	C₄×Dic₆₁	—	8	2	no	—
69	C₂×#92418	—	2	4	no	—
70	C₂×#92418	—	4	2	no	—
71	C₂×#92418	—	4	2	no	—
72	C₂³×C₆₁	#120	1	1	yes	characteristic
73	Q₈×C₆₁	—	4	4	no	—
74	Q₈×C₆₁	—	8	2	no	—
75	C₂×C₄×C₆₁	—	2	1	no	—
76	C₂×C₄×C₆₁	—	2	1	no	—
77	C₂×C₄×C₆₁	—	2	4	no	—
78	C₂×C₄×C₆₁	—	4	2	no	—
79	C₂×C₄×C₆₁	—	4	2	no	—
80	C₂×C₄×C₆₁	—	8	2	no	—
81	C₂×C₄×C₆₁	—	8	1	no	—
82	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
86	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
87	C₂×C₄×C₆₁	#135	1	2	yes	—
88	C₂×C₄×C₆₁	#137	1	2	yes	—
89	C₂×C₄×C₆₁	#137	1	2	yes	—
90	C₂×Dic₆₁	—	2	4	no	—
91	C₂×Dic₆₁	—	4	2	no	—
92	C₂×Dic₆₁	—	4	2	no	—
93	C₂×Dic₆₁	—	4	2	no	—
94	C₂×Dic₆₁	—	4	2	no	—
95	C₂×Dic₆₁	—	4	2	no	—
96	C₈×C₆₁	—	4	2	no	—
97	#92418	—	4	4	no	—
98	#8928	—	61	1	no	maximal, Sylow
99	C₂²×C₆₁	#385	1	1	yes	characteristic
100	C₂²×C₆₁	#448	1	2	yes	—
101	C₂²×C₆₁	#452	1	2	yes	—
102	C₂²×C₆₁	#453	1	1	yes	characteristic
103	C₂²×C₆₁	#455	1	1	yes	characteristic
104	C₄×C₆₁	—	2	1	no	—
105	C₄×C₆₁	—	2	1	no	—
106	C₄×C₆₁	—	4	4	no	—
107	C₄×C₆₁	—	16	1	no	—
108	C₄×C₆₁	C₄×SD₁₆	1	2	yes	—
109	C₄×C₆₁	#441	1	2	yes	—
110	C₄×C₆₁	#475	1	2	yes	—
111	C₄×C₆₁	#479	1	2	yes	—
112	Dic₆₁	—	4	4	no	—
113	Dic₆₁	—	8	2	no	—
114	#2369	—	61	1	no	—
115	#1956	D₆₁	1	1	yes	characteristic
116	#1948	—	61	2	no	—
117	C₂×#333	—	61	1	no	—
118	#1279	—	61	2	no	—
119	C₂×C₆₁	#1623	1	1	yes	characteristic
120	C₂×C₆₁	#1634	1	1	yes	characteristic
121	C₂×C₆₁	#1643	1	2	yes	—
122	C₂×C₆₁	#1856	1	1	yes	characteristic
123	C₂×C₆₁	#1865	1	2	yes	—
124	C₂×C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
125	C₂×#106	—	122	2	no	—
126	C₂×C₄⋊C₈	—	61	2	no	—
127	C₂×#103	—	2	2	no	—
128	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
129	#391	—	122	2	no	—
130	#389	—	122	2	no	—
131	#384	C₂×D₆₁	1	1	yes	characteristic
132	C₄×C₄⋊C₄	—	61	2	no	—
133	C₄×C₄⋊C₄	—	122	2	no	—
134	#340	—	122	2	no	—
135	#333	—	61	4	no	—
136	C₆₁	#8928	1	1	yes	characteristic, complemented, Sylow
137	C₂²×Q₈	C₂²⋊D₆₁	1	2	yes	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	—	122	2	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	Dic₁₂₂	1	2	yes	—
142	C₄⋊Q₈	C₄×D₆₁	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	2	2	no	—
145	C₂×C₄⋊C₄	—	2	1	no	—
146	C₂×C₄⋊C₄	—	61	2	no	—
147	C₂×C₄⋊C₄	—	61	2	no	—
148	C₂×C₄⋊C₄	—	122	2	no	—
149	C₂×C₄²	—	122	2	no	—
150	C₂×C₄²	—	122	2	no	—
151	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
152	#106	—	244	4	no	—
153	C₄⋊C₈	—	61	4	no	—
154	C₄⋊C₈	—	122	2	no	—
155	#103	—	4	4	no	—
156	C₄×C₈	—	2	2	no	—
157	#95	—	122	4	no	—
158	#95	—	122	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	4	2	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	#11758196	1	4	yes	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	4	1	no	—
165	C₂²×C₄	—	122	2	no	—
166	C₂²×C₄	—	122	2	no	—
167	C₂²×C₄	D₄×D₆₁	1	2	yes	—
168	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	1	no	—
171	C₂×C₈	—	4	1	no	—
172	C₂×C₈	—	122	4	no	—
173	C₂×C₈	—	244	2	no	—
174	C₂×C₈	—	244	2	no	—
175	C₄⋊C₄	—	2	4	no	—
176	C₄⋊C₄	—	2	4	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	61	4	no	—
181	C₄⋊C₄	—	122	2	no	—
182	C₄⋊C₄	—	122	2	no	—
183	C₄⋊C₄	—	122	2	no	—
184	C₄⋊C₄	—	488	2	no	—
185	C₄²	—	488	2	no	—
186	C₄²	—	244	2	no	—
187	C₄²	—	244	2	no	—
188	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
190	C₄²	#11758224	1	2	yes	—
191	C₂³	#14519745	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	8	2	no	—
200	C₂×C₄	—	8	1	no	—
201	C₂×C₄	—	122	4	no	—
202	C₂×C₄	—	244	2	no	—
203	C₂×C₄	—	244	2	no	—
204	C₂×C₄	—	244	2	no	—
205	C₂×C₄	—	244	2	no	—
206	C₂×C₄	—	244	2	no	—
207	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
208	C₂×C₄	#14519737	1	2	yes	—
209	C₂×C₄	#14519754	1	2	yes	—
210	C₂×C₄	#14519758	1	1	yes	characteristic
211	C₂×C₄	SD₁₆×D₆₁	1	2	yes	—
212	C₂×C₄	#14519800	1	2	yes	—
213	C₂×C₄	#14519806	1	2	yes	—
214	C₂×C₄	#14519809	1	2	yes	—
215	C₈	—	4	2	no	—
216	C₈	—	244	4	no	—
217	C₂²	#16839634	1	1	yes	characteristic
218	C₂²	#16839899	1	2	yes	—
219	C₂²	#16839923	1	2	yes	—
220	C₂²	#16839929	1	1	yes	characteristic
221	C₂²	#16839939	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	4	no	—
225	C₄	—	16	1	no	—
226	C₄	—	488	2	no	—
227	C₄	—	244	4	no	—
228	C₄	#16839847	1	2	yes	—
229	C₄	#16839866	1	2	yes	—
230	C₄	#16840045	1	2	yes	—
231	C₄	#16840071	1	2	yes	—
232	C₂	#21444895	1	1	yes	characteristic
233	C₂	#21444962	1	1	yes	characteristic
234	C₂	#21445023	1	2	yes	—
235	C₂	#21446028	1	1	yes	characteristic
236	C₂	#21446085	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#21448909

C₂

yes

maximal, characteristic

#21446580

C₂

yes

maximal

C₂×#16839511

C₂

yes

maximal, characteristic

#21443659

C₂

yes

maximal

C₆₁×#1956

C₂

yes

maximal, characteristic

C₂×#14519708

—

C₂×C₄⋊#92418

C₂²

yes

—

#16839669

—

#16839661

—

C₄⋊C₄×Dic₆₁

—

C₄×C₄⋊Dic₆₁

C₂²

yes

—

#16839524

—

#16839511

C₄

yes

complemented

C₂×C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

C₂×#103×C₆₁

—

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₆₁×#384

C₂²

yes

characteristic

C₂²×#92418

—

C₂×C₄⋊Dic₆₁

—

C₂×C₄⋊Dic₆₁

D₄

yes

—

C₂×C₄⋊Dic₆₁

D₄

yes

—

C₂×C₄×Dic₆₁

—

C₂×C₄×Dic₆₁

—

#14519708

—

C₄⋊#92418

—

C₄⋊#92418

C₂×C₄

yes

—

#14519684

—

#14519684

—

C₂²×Q₈×C₆₁

D₄

yes

—

C₂²×C₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

C₂×C₄

yes

—

C₄⋊Q₈×C₆₁

Q₈

yes

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

#103×C₆₁

—

C₄×C₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

C₄⋊C₄

yes

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

—

C₂²×Dic₆₁

—

C₂²×Dic₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄²×C₆₁

C₂×Q₈

yes

characteristic

C₄²×C₆₁

#41

yes

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

SD₁₆

yes

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₂×#92418

—

C₂×#92418

—

C₂×#92418

—

C₂³×C₆₁

#120

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄×D₄

yes

—

C₂×C₄×C₆₁

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₁

#123

yes

characteristic

C₂×C₄×C₆₁

C₂×SD₁₆

yes

—

C₂×C₄×C₆₁

#135

yes

—

C₂×C₄×C₆₁

#137

yes

—

C₂×C₄×C₆₁

#137

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

—

—

C₂²×C₆₁

yes

100

C₂²×C₆₁

#448

yes

—

101

C₂²×C₆₁

#452

yes

—

102

C₂²×C₆₁

#453

yes

characteristic

103

C₂²×C₆₁

#455

yes

characteristic

104

C₄×C₆₁

—

105

C₄×C₆₁

—

106

C₄×C₆₁

—

107

C₄×C₆₁

—

108

C₄×C₆₁

C₄×SD₁₆

yes

—

109

C₄×C₆₁

#441

yes

—

110

C₄×C₆₁

#475

yes

—

111

C₄×C₆₁

#479

yes

—

112

Dic₆₁

—

113

Dic₆₁

—

114

#2369

—

115

#1956

D₆₁

yes

characteristic

116

#1948

—

117

C₂×#333

—

118

#1279

—

119

C₂×C₆₁

#1623

yes

characteristic

120

C₂×C₆₁

#1634

yes

characteristic

121

C₂×C₆₁

#1643

yes

—

122

C₂×C₆₁

#1856

yes

characteristic

123

C₂×C₆₁

#1865

yes

—

124

C₂×C₄⋊Q₈

C₂×D₆₁

yes

characteristic

125

C₂×#106

—

122

—

126

C₂×C₄⋊C₈

—

127

C₂×#103

—

128

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

129

#391

—

122

—

130

#389

—

122

—

131

#384

C₂×D₆₁

yes

characteristic

132

C₄×C₄⋊C₄

—

133

C₄×C₄⋊C₄

—

122

—

134

#340

—

122

—

135

#333

—

136

C₆₁

#8928

yes

characteristic, complemented, Sylow

137

C₂²×Q₈

C₂²⋊D₆₁

yes

—

138

C₂²×C₈

—

139

C₂²×C₈

—

122

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

Dic₁₂₂

yes

—

142

C₄⋊Q₈

C₄×D₆₁

yes

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

122

—

149

C₂×C₄²

—

122

—

150

C₂×C₄²

—

122

—

151

C₂×C₄²

C₂²×D₆₁

yes

characteristic

152

#106

—

244

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

122

—

155

#103

—

156

C₄×C₈

—

157

#95

—

122

—

158

#95

—

122

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

#11758196

yes

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

122

—

166

C₂²×C₄

—

122

—

167

C₂²×C₄

D₄×D₆₁

yes

—

168

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

122

—

173

C₂×C₈

—

244

—

174

C₂×C₈

—

244

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

122

—

182

C₄⋊C₄

—

122

—

183

C₄⋊C₄

—

122

—

184

C₄⋊C₄

—

488

—

185

C₄²

—

488

—

186

C₄²

—

244

—

187

C₄²

—

244

—

188

C₄²

C₂×Dic₁₂₂

yes

characteristic

189

C₄²

C₂×C₄×D₆₁

yes

characteristic

190

C₄²

#11758224

yes

—

191

C₂³

#14519745

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

122

—

202

C₂×C₄

—

244

—

203

C₂×C₄

—

244

—

204

C₂×C₄

—

244

—

205

C₂×C₄

—

244

—

206

C₂×C₄

—

244

—

207

C₂×C₄

C₂×#11758196

yes

characteristic

208

C₂×C₄

#14519737

yes

—

209

C₂×C₄

#14519754

yes

—

210

C₂×C₄

#14519758

yes

characteristic

211

C₂×C₄

SD₁₆×D₆₁

yes

—

212

C₂×C₄

#14519800

yes

—

213

C₂×C₄

#14519806

yes

—

214

C₂×C₄

#14519809

yes

—

215

C₈

—

216

C₈

—

244

—

217

C₂²

#16839634

yes

characteristic

218

C₂²

#16839899

yes

—

219

C₂²

#16839923

yes

—

220

C₂²

#16839929

yes

characteristic

221

C₂²

#16839939

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

488

—

227

C₄

—

244

—

228

C₄

#16839847

yes

—

229

C₄

#16839866

yes

—

230

C₄

#16840045

yes

—

231

C₄

#16840071

yes

—

232

C₂

#21444895

yes

characteristic

233

C₂

#21444962

yes

characteristic

234

C₂

#21445023

yes

—

235

C₂

#21446028

yes

characteristic

236

C₂

#21446085

yes

—

	subgroup	G/H
center	C₂³	#14519745
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₆₁×#1956	C₂
socle, prime radical	C₂³×C₆₁	#120
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#1956	D₆₁
hypocenter	C₆₁	#8928
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

subgroup

G/H

center

C₂³

#14519745

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₆₁×#1956

C₂

socle, prime radical

C₂³×C₆₁

#120

cosocle

C₂×C₄²×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

N	H ≅ G/N	type
13. #16839511	C₄	semidirect
136. C₆₁	#8928	semidirect

H ≅ G/N

type

13. #16839511

C₄

semidirect

136. C₆₁

#8928

semidirect

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

subgroup	index
#21448909	2
#21446580	2
C₂×#16839511	2
#21443659	2
C₆₁×#1956	2
#8928	61

subgroup

index

C₆₁×#1956

Subgroups — #29574477

Conjugacy classes of subgroups

Complements

Maximal subgroups