Group #29516748 — subgroups

Subgroups — C₆₁×#13315 #29516748

Order 15616.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₂²×Q₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#473	C₂	1	2	yes	maximal
3	C₂×C₆₁×#362	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2113	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1381	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#137×C₆₁	—	2	2	no	—
7	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
8	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×Q₃₂×C₆₁	—	2	4	no	—
10	C₂×Q₃₂×C₆₁	—	2	2	no	—
11	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#473	—	2	4	no	—
14	C₆₁×#473	—	2	4	no	—
15	C₂×#108×C₆₁	C₂²	1	2	yes	—
16	C₂×#101×C₆₁	—	2	2	no	—
17	C₆₁×#362	—	2	4	no	—
18	C₆₁×C₂²⋊C₁₆	—	2	2	no	—
19	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
20	C₂²×Q₈×C₆₁	—	2	2	no	—
21	#137×C₆₁	—	2	8	no	—
22	#137×C₆₁	—	4	4	no	—
23	C₂×Q₁₆×C₆₁	—	2	2	no	—
24	C₂×Q₁₆×C₆₁	—	2	2	no	—
25	C₂×Q₁₆×C₆₁	—	2	2	no	—
26	C₂×Q₁₆×C₆₁	—	2	2	no	—
27	C₂×Q₁₆×C₆₁	—	2	2	no	—
28	C₂×Q₁₆×C₆₁	—	4	2	no	—
29	C₂×Q₁₆×C₆₁	D₄	1	4	yes	—
30	C₂×SD₁₆×C₆₁	—	4	2	no	—
31	#131×C₆₁	—	2	2	no	—
32	#131×C₆₁	—	2	2	no	—
33	C₂×M₁₆×C₆₁	—	2	1	no	—
34	C₂×M₁₆×C₆₁	—	2	2	no	—
35	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₆₁	—	2	1	no	—
37	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
38	Q₃₂×C₆₁	—	2	8	no	—
39	M₃₂×C₆₁	—	2	2	no	—
40	C₂×C₁₆×C₆₁	—	2	2	no	—
41	C₂×C₁₆×C₆₁	—	2	1	no	—
42	C₂×C₁₆×C₆₁	D₄	1	2	yes	—
43	#108×C₆₁	—	2	2	no	—
44	#108×C₆₁	D₄	1	4	yes	—
45	#101×C₆₁	—	2	8	no	—
46	#41×C₆₁	—	2	2	no	—
47	#41×C₆₁	—	2	2	no	—
48	C₂×Q₈×C₆₁	—	2	4	no	—
49	C₂×Q₈×C₆₁	—	4	2	no	—
50	C₂×Q₈×C₆₁	—	4	2	no	—
51	C₂×Q₈×C₆₁	—	4	2	no	—
52	C₂×Q₈×C₆₁	—	4	2	no	—
53	C₂×Q₈×C₆₁	—	4	2	no	—
54	C₂×Q₈×C₆₁	D₈	1	1	yes	characteristic
55	C₂×D₄×C₆₁	—	2	1	no	—
56	C₂×D₄×C₆₁	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₆₁	—	2	1	no	—
58	C₂²×C₄×C₆₁	—	4	2	no	—
59	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
60	Q₁₆×C₆₁	—	2	4	no	—
61	Q₁₆×C₆₁	—	2	4	no	—
62	Q₁₆×C₆₁	—	4	8	no	—
63	Q₁₆×C₆₁	—	4	2	no	—
64	Q₁₆×C₆₁	—	4	2	no	—
65	SD₁₆×C₆₁	—	4	8	no	—
66	M₁₆×C₆₁	—	2	2	no	—
67	M₁₆×C₆₁	—	2	4	no	—
68	M₁₆×C₆₁	—	4	2	no	—
69	M₁₆×C₆₁	—	4	2	no	—
70	C₂×C₈×C₆₁	—	2	1	no	—
71	C₂×C₈×C₆₁	—	4	2	no	—
72	C₂×C₈×C₆₁	—	4	1	no	—
73	C₂×C₈×C₆₁	—	4	1	no	—
74	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
78	C₁₆×C₆₁	—	2	2	no	—
79	C₁₆×C₆₁	—	4	1	no	—
80	C₂³×C₆₁	—	2	1	no	—
81	C₂³×C₆₁	#135	1	1	yes	characteristic
82	Q₈×C₆₁	—	2	2	no	—
83	Q₈×C₆₁	—	4	4	no	—
84	Q₈×C₆₁	—	4	4	no	—
85	Q₈×C₆₁	—	8	2	no	—
86	Q₈×C₆₁	—	8	2	no	—
87	D₄×C₆₁	—	2	2	no	—
88	D₄×C₆₁	—	4	2	no	—
89	C₂×C₄×C₆₁	—	2	1	no	—
90	C₂×C₄×C₆₁	—	4	1	no	—
91	C₂×C₄×C₆₁	—	4	1	no	—
92	C₂×C₄×C₆₁	—	4	4	no	—
93	C₂×C₄×C₆₁	—	8	2	no	—
94	C₂×C₄×C₆₁	—	8	2	no	—
95	C₂×C₄×C₆₁	#120	1	2	yes	—
96	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
97	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
98	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
99	C₈×C₆₁	—	4	1	no	—
100	C₈×C₆₁	—	4	4	no	—
101	C₈×C₆₁	#120	1	1	yes	characteristic
102	C₈×C₆₁	#121	1	2	yes	—
103	C₈×C₆₁	#127	1	1	yes	characteristic
104	#13315	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂²×C₆₁	—	2	2	no	—
106	C₂²×C₆₁	—	4	2	no	—
107	C₂²×C₆₁	—	4	1	no	—
108	C₂²×C₆₁	#449	1	2	yes	—
109	C₂²×C₆₁	#466	1	1	yes	characteristic
110	C₄×C₆₁	—	4	1	no	—
111	C₄×C₆₁	—	8	4	no	—
112	C₄×C₆₁	#392	1	1	yes	characteristic
113	C₄×C₆₁	#447	1	2	yes	—
114	C₄×C₆₁	#469	1	1	yes	characteristic
115	C₂²×Q₃₂	C₂×C₆₁	1	1	yes	characteristic, complemented
116	C₂×#473	C₂×C₆₁	1	2	yes	—
117	C₂×#362	C₂×C₆₁	1	2	yes	complemented
118	#2113	C₂×C₆₁	1	1	yes	characteristic
119	#1381	C₂×C₆₁	1	1	yes	characteristic, complemented
120	C₂×C₆₁	—	2	2	no	—
121	C₂×C₆₁	—	8	1	no	—
122	C₂×C₆₁	#1999	1	1	yes	characteristic
123	C₂×C₆₁	#2222	1	2	yes	—
124	C₂×#137	—	2	2	no	—
125	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
126	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
127	C₂×Q₃₂	—	2	4	no	—
128	C₂×Q₃₂	—	2	2	no	—
129	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
130	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
131	#473	—	2	4	no	—
132	#473	—	2	4	no	—
133	C₂×#108	C₂²×C₆₁	1	2	yes	—
134	C₂×#101	—	2	2	no	—
135	#362	—	2	4	no	—
136	C₂²⋊C₁₆	—	2	2	no	—
137	C₆₁	#13315	1	1	yes	characteristic, direct product factor, Sylow
138	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
139	C₂²×Q₈	—	2	2	no	—
140	#137	—	2	8	no	—
141	#137	—	4	4	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	—	2	2	no	—
144	C₂×Q₁₆	—	2	2	no	—
145	C₂×Q₁₆	—	2	2	no	—
146	C₂×Q₁₆	—	2	2	no	—
147	C₂×Q₁₆	—	4	2	no	—
148	C₂×Q₁₆	D₄×C₆₁	1	4	yes	—
149	C₂×SD₁₆	—	4	2	no	—
150	#131	—	2	2	no	—
151	#131	—	2	2	no	—
152	C₂×M₁₆	—	2	1	no	—
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
157	Q₃₂	—	2	8	no	—
158	M₃₂	—	2	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	—	2	1	no	—
161	C₂×C₁₆	D₄×C₆₁	1	2	yes	—
162	#108	—	2	2	no	—
163	#108	D₄×C₆₁	1	4	yes	—
164	#101	—	2	8	no	—
165	#41	—	2	2	no	—
166	#41	—	2	2	no	—
167	C₂×Q₈	—	2	4	no	—
168	C₂×Q₈	—	4	2	no	—
169	C₂×Q₈	—	4	2	no	—
170	C₂×Q₈	—	4	2	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	2	no	—
173	C₂×Q₈	D₈×C₆₁	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	D₈×C₆₁	1	1	yes	characteristic
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
179	Q₁₆	—	2	4	no	—
180	Q₁₆	—	2	4	no	—
181	Q₁₆	—	4	8	no	—
182	Q₁₆	—	4	2	no	—
183	Q₁₆	—	4	2	no	—
184	SD₁₆	—	4	8	no	—
185	M₁₆	—	2	2	no	—
186	M₁₆	—	2	4	no	—
187	M₁₆	—	4	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	4	2	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	4	1	no	—
193	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
194	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
195	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
196	C₂×C₈	#41×C₆₁	1	1	yes	characteristic
197	C₁₆	—	2	2	no	—
198	C₁₆	—	4	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	#135×C₆₁	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	4	4	no	—
203	Q₈	—	4	4	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	8	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	4	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	8	2	no	—
213	C₂×C₄	—	8	2	no	—
214	C₂×C₄	#120×C₆₁	1	2	yes	—
215	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
216	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
217	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
218	C₈	—	4	1	no	—
219	C₈	—	4	4	no	—
220	C₈	#120×C₆₁	1	1	yes	characteristic
221	C₈	#121×C₆₁	1	2	yes	—
222	C₈	#127×C₆₁	1	1	yes	characteristic
223	C₂²	—	2	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	1	no	—
226	C₂²	C₆₁×#449	1	2	yes	—
227	C₂²	C₆₁×#466	1	1	yes	characteristic
228	C₄	—	4	1	no	—
229	C₄	—	8	4	no	—
230	C₄	C₆₁×#392	1	1	yes	characteristic
231	C₄	C₆₁×#447	1	2	yes	—
232	C₄	C₆₁×#469	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	—	8	1	no	—
235	C₂	C₆₁×#1999	1	1	yes	characteristic
236	C₂	C₆₁×#2222	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₃₂×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×C₆₁×#473

C₂

yes

maximal

C₂×C₆₁×#362

C₂

yes

maximal, complemented

C₆₁×#2113

C₂

yes

maximal, characteristic

C₆₁×#1381

C₂

yes

maximal, characteristic, complemented

C₂×#137×C₆₁

—

C₂²×Q₁₆×C₆₁

C₂²

yes

—

C₂×#131×C₆₁

C₂²

yes

characteristic

C₂×Q₃₂×C₆₁

—

C₂×Q₃₂×C₆₁

—

C₂×M₃₂×C₆₁

C₂²

yes

characteristic

C₂²×C₁₆×C₆₁

C₂²

yes

characteristic

C₆₁×#473

—

C₆₁×#473

—

C₂×#108×C₆₁

C₂²

yes

—

C₂×#101×C₆₁

—

C₆₁×#362

—

C₆₁×C₂²⋊C₁₆

—

C₂×#41×C₆₁

D₄

yes

characteristic

C₂²×Q₈×C₆₁

—

#137×C₆₁

—

#137×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

—

C₂×Q₁₆×C₆₁

D₄

yes

—

C₂×SD₁₆×C₆₁

—

#131×C₆₁

—

#131×C₆₁

—

C₂×M₁₆×C₆₁

—

C₂×M₁₆×C₆₁

—

C₂×M₁₆×C₆₁

D₄

yes

characteristic

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

C₂³

yes

characteristic

Q₃₂×C₆₁

—

M₃₂×C₆₁

—

C₂×C₁₆×C₆₁

—

C₂×C₁₆×C₆₁

—

C₂×C₁₆×C₆₁

D₄

yes

—

#108×C₆₁

—

#108×C₆₁

D₄

yes

—

#101×C₆₁

—

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

D₈

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

D₈

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

Q₁₆×C₆₁

—

SD₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×D₄

yes

—

C₂×C₈×C₆₁

C₂×D₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

—

C₂×C₈×C₆₁

#41

yes

characteristic

C₁₆×C₆₁

—

C₁₆×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

#135

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

#120

yes

—

C₂×C₄×C₆₁

#121

yes

characteristic

C₂×C₄×C₆₁

C₂×D₈

yes

characteristic

C₂×C₄×C₆₁

AGL(1,ℤ/8)

yes

—

C₈×C₆₁

—

100

C₈×C₆₁

—

101

C₈×C₆₁

#120

yes

characteristic

102

C₈×C₆₁

#121

yes

—

103

C₈×C₆₁

#127

yes

characteristic

104

#13315

C₆₁

yes

maximal, characteristic, direct product factor, Sylow

105

C₂²×C₆₁

—

106

C₂²×C₆₁

—

107

C₂²×C₆₁

—

108

C₂²×C₆₁

#449

yes

—

109

C₂²×C₆₁

#466

yes

characteristic

110

C₄×C₆₁

—

111

C₄×C₆₁

—

112

C₄×C₆₁

#392

yes

characteristic

113

C₄×C₆₁

#447

yes

—

114

C₄×C₆₁

#469

yes

characteristic

115

C₂²×Q₃₂

C₂×C₆₁

yes

characteristic, complemented

116

C₂×#473

C₂×C₆₁

yes

—

117

C₂×#362

C₂×C₆₁

yes

complemented

118

#2113

C₂×C₆₁

yes

characteristic

119

#1381

C₂×C₆₁

yes

characteristic, complemented

120

C₂×C₆₁

—

121

C₂×C₆₁

—

122

C₂×C₆₁

#1999

yes

characteristic

123

C₂×C₆₁

#2222

yes

—

124

C₂×#137

—

125

C₂²×Q₁₆

C₂²×C₆₁

yes

—

126

C₂×#131

C₂²×C₆₁

yes

characteristic

127

C₂×Q₃₂

—

128

C₂×Q₃₂

—

129

C₂×M₃₂

C₂²×C₆₁

yes

characteristic

130

C₂²×C₁₆

C₂²×C₆₁

yes

characteristic

131

#473

—

132

#473

—

133

C₂×#108

C₂²×C₆₁

yes

—

134

C₂×#101

—

135

#362

—

136

C₂²⋊C₁₆

—

137

C₆₁

#13315

yes

characteristic, direct product factor, Sylow

138

C₂×#41

D₄×C₆₁

yes

characteristic

139

C₂²×Q₈

—

140

#137

—

141

#137

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

D₄×C₆₁

yes

—

149

C₂×SD₁₆

—

150

#131

—

151

#131

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

154

C₂×M₁₆

D₄×C₆₁

yes

characteristic

155

C₂²×C₈

—

156

C₂²×C₈

C₂³×C₆₁

yes

characteristic

157

Q₃₂

—

158

M₃₂

—

159

C₂×C₁₆

—

160

C₂×C₁₆

—

161

C₂×C₁₆

D₄×C₆₁

yes

—

162

#108

—

163

#108

D₄×C₆₁

yes

—

164

#101

—

165

#41

—

166

#41

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

D₈×C₆₁

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

D₈×C₆₁

yes

characteristic

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

C₂×D₄×C₆₁

yes

characteristic

179

Q₁₆

—

180

Q₁₆

—

181

Q₁₆

—

182

Q₁₆

—

183

Q₁₆

—

184

SD₁₆

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

193

C₂×C₈

C₂×D₄×C₆₁

yes

—

194

C₂×C₈

C₂×D₄×C₆₁

yes

characteristic

195

C₂×C₈

C₂×D₄×C₆₁

yes

—

196

C₂×C₈

#41×C₆₁

yes

characteristic

197

C₁₆

—

198

C₁₆

—

199

C₂³

—

200

C₂³

#135×C₆₁

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

#120×C₆₁

yes

—

215

C₂×C₄

#121×C₆₁

yes

characteristic

216

C₂×C₄

C₂×D₈×C₆₁

yes

characteristic

217

C₂×C₄

AGL(1,ℤ/8)×C₆₁

yes

—

218

C₈

—

219

C₈

—

220

C₈

#120×C₆₁

yes

characteristic

221

C₈

#121×C₆₁

yes

—

222

C₈

#127×C₆₁

yes

characteristic

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

C₆₁×#449

yes

—

227

C₂²

C₆₁×#466

yes

characteristic

228

C₄

—

229

C₄

—

230

C₄

C₆₁×#392

yes

characteristic

231

C₄

C₆₁×#447

yes

—

232

C₄

C₆₁×#469

yes

characteristic

233

C₂

—

234

C₂

—

235

C₂

C₆₁×#1999

yes

characteristic

236

C₂

C₆₁×#2222

yes

—

	subgroup	G/H
center, socle	C₂²×C₆₁	#466
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₆₁
prime radical	C₂×#41×C₆₁	D₄
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂×#131×C₆₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₆₁

#466

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₆₁

prime radical

C₂×#41×C₆₁

D₄

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂×#131×C₆₁ ◁ G

N	H ≅ G/N	type
1. C₂²×Q₃₂×C₆₁	C₂	semidirect
3. C₂×C₆₁×#362	C₂	semidirect
5. C₆₁×#1381	C₂	semidirect
104. #13315	C₆₁	direct (N × H)
115. C₂²×Q₃₂	C₂×C₆₁	semidirect
117. C₂×#362	C₂×C₆₁	semidirect
119. #1381	C₂×C₆₁	semidirect
137. C₆₁	#13315	direct (N × H)

H ≅ G/N

type

1. C₂²×Q₃₂×C₆₁

C₂

semidirect

3. C₂×C₆₁×#362

C₂

semidirect

5. C₆₁×#1381

C₂

semidirect

104. #13315

C₆₁

direct (N × H)

115. C₂²×Q₃₂

C₂×C₆₁

semidirect

117. C₂×#362

C₂×C₆₁

semidirect

119. #1381

C₂×C₆₁

semidirect

137. C₆₁

#13315

direct (N × H)

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

subgroup	index
C₂²×Q₃₂×C₆₁	2
C₂×C₆₁×#473	2
C₂×C₆₁×#362	2
C₆₁×#2113	2
C₆₁×#1381	2
#13315	61

subgroup

index

C₂²×Q₃₂×C₆₁

C₂×C₆₁×#473

C₂×C₆₁×#362

C₆₁×#2113

C₆₁×#1381

#13315

Subgroups — C₆₁×#13315 #29516748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C61×#13315 #29516748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#13315 #29516748