Group #29512833 — subgroups

Subgroups — C₆₁×#9400 #29512833

Order 15616.

466 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₆₁×#2983	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2567	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1801	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1548	C₂	1	2	yes	maximal
5	C₆₁×#1303	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
8	C₆₁×#446	—	2	4	no	—
9	C₆₁×#432	—	2	2	no	—
10	C₆₁×#431	C₂²	1	2	yes	—
11	C₆₁×#423	C₂²	1	2	yes	—
12	C₂×#101×C₆₁	—	2	1	no	—
13	C₆₁×#395	C₄	1	4	yes	—
14	C₆₁×#391	—	2	1	no	—
15	C₆₁×#389	—	2	2	no	—
16	C₆₁×#384	—	2	1	no	—
17	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#343	—	2	1	no	—
19	C₆₁×#333	—	2	4	no	—
20	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
21	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₆₁	—	2	2	no	—
23	C₄⋊Q₈×C₆₁	—	2	2	no	—
24	C₄⋊Q₈×C₆₁	—	2	2	no	—
25	C₄×Q₈×C₆₁	—	2	2	no	—
26	C₄×Q₈×C₆₁	—	2	2	no	—
27	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
28	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
29	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
30	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
31	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₆₁	—	2	1	no	—
34	C₂×C₄²×C₆₁	D₄	1	2	yes	—
35	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₆₁	—	2	4	no	—
37	C₄⋊C₈×C₆₁	—	2	2	no	—
38	C₄⋊C₈×C₆₁	—	2	2	no	—
39	C₄⋊C₈×C₆₁	D₄	1	4	yes	—
40	#101×C₆₁	—	4	2	no	—
41	C₂²⋊C₈×C₆₁	—	2	2	no	—
42	#97×C₆₁	—	2	4	no	—
43	C₄×C₈×C₆₁	—	2	2	no	—
44	#95×C₆₁	—	2	4	no	—
45	#95×C₆₁	C₂×C₄	1	2	yes	—
46	C₂×Q₈×C₆₁	—	2	2	no	—
47	C₂×Q₈×C₆₁	—	2	1	no	—
48	C₂×Q₈×C₆₁	—	2	1	no	—
49	C₂×Q₈×C₆₁	—	2	2	no	—
50	C₂×Q₈×C₆₁	—	2	4	no	—
51	C₂×Q₈×C₆₁	—	8	2	no	—
52	C₂²×C₄×C₆₁	—	2	2	no	—
53	C₂²×C₄×C₆₁	—	2	2	no	—
54	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
59	M₁₆×C₆₁	—	4	2	no	—
60	M₁₆×C₆₁	—	4	2	no	—
61	C₂×C₈×C₆₁	—	2	4	no	—
62	C₂×C₈×C₆₁	—	4	2	no	—
63	C₄⋊C₄×C₆₁	—	2	4	no	—
64	C₄⋊C₄×C₆₁	—	2	4	no	—
65	C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₄⋊C₄×C₆₁	—	4	1	no	—
67	C₄⋊C₄×C₆₁	—	4	2	no	—
68	C₄⋊C₄×C₆₁	—	4	1	no	—
69	C₄⋊C₄×C₆₁	—	8	4	no	—
70	C₄²×C₆₁	—	2	2	no	—
71	C₄²×C₆₁	—	2	2	no	—
72	C₄²×C₆₁	—	4	1	no	—
73	C₄²×C₆₁	—	4	1	no	—
74	C₄²×C₆₁	C₂×D₄	1	2	yes	—
75	C₄²×C₆₁	#41	1	2	yes	—
76	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	Q₈×C₆₁	—	4	2	no	—
78	Q₈×C₆₁	—	4	2	no	—
79	Q₈×C₆₁	—	8	4	no	—
80	C₂×C₄×C₆₁	—	2	2	no	—
81	C₂×C₄×C₆₁	—	2	4	no	—
82	C₂×C₄×C₆₁	—	2	2	no	—
83	C₂×C₄×C₆₁	—	2	2	no	—
84	C₂×C₄×C₆₁	—	2	2	no	—
85	C₂×C₄×C₆₁	—	2	2	no	—
86	C₂×C₄×C₆₁	—	4	1	no	—
87	C₂×C₄×C₆₁	—	4	2	no	—
88	C₂×C₄×C₆₁	—	4	2	no	—
89	C₂×C₄×C₆₁	—	4	2	no	—
90	C₂×C₄×C₆₁	—	4	4	no	—
91	C₂×C₄×C₆₁	—	4	2	no	—
92	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
94	C₂×C₄×C₆₁	#121	1	2	yes	—
95	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
96	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
97	C₂×C₄×C₆₁	#137	1	2	yes	—
98	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
99	C₈×C₆₁	—	4	4	no	—
100	C₈×C₆₁	—	8	2	no	—
101	#9400	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂²×C₆₁	—	2	1	no	—
103	C₂²×C₆₁	—	2	1	no	—
104	C₂²×C₆₁	#386	1	1	yes	characteristic
105	C₂²×C₆₁	#417	1	1	yes	characteristic
106	C₂²×C₆₁	#419	1	1	yes	characteristic
107	C₄×C₆₁	—	2	1	no	—
108	C₄×C₆₁	—	2	2	no	—
109	C₄×C₆₁	—	4	4	no	—
110	C₄×C₆₁	—	4	2	no	—
111	C₄×C₆₁	—	4	2	no	—
112	C₄×C₆₁	—	8	2	no	—
113	C₄×C₆₁	#456	1	2	yes	—
114	C₄×C₆₁	#468	1	2	yes	—
115	C₄×C₆₁	#470	1	2	yes	—
116	#2983	C₂×C₆₁	1	1	yes	characteristic
117	#2567	C₂×C₆₁	1	1	yes	characteristic
118	#1801	C₂×C₆₁	1	1	yes	characteristic
119	#1548	C₂×C₆₁	1	2	yes	—
120	#1303	C₂×C₆₁	1	2	yes	—
121	C₂×C₆₁	—	2	1	no	—
122	C₂×C₆₁	—	2	1	no	—
123	C₂×C₆₁	#1886	1	1	yes	characteristic
124	C₂×C₆₁	#1894	1	1	yes	characteristic
125	C₂×C₆₁	#1914	1	1	yes	characteristic
126	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
127	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
128	#446	—	2	4	no	—
129	#432	—	2	2	no	—
130	#431	C₂²×C₆₁	1	2	yes	—
131	#423	C₂²×C₆₁	1	2	yes	—
132	C₂×#101	—	2	1	no	—
133	#395	C₄×C₆₁	1	4	yes	—
134	#391	—	2	1	no	—
135	#389	—	2	2	no	—
136	#384	—	2	1	no	—
137	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
138	#343	—	2	1	no	—
139	#333	—	2	4	no	—
140	C₆₁	#9400	1	1	yes	characteristic, direct product factor, Sylow
141	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
142	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
143	C₂×M₁₆	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
153	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
154	C₂×C₄²	—	2	1	no	—
155	C₂×C₄²	D₄×C₆₁	1	2	yes	—
156	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
157	C₄⋊C₈	—	2	4	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	D₄×C₆₁	1	4	yes	—
161	#101	—	4	2	no	—
162	C₂²⋊C₈	—	2	2	no	—
163	#97	—	2	4	no	—
164	C₄×C₈	—	2	2	no	—
165	#95	—	2	4	no	—
166	#95	C₂×C₄×C₆₁	1	2	yes	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	1	no	—
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	2	4	no	—
172	C₂×Q₈	—	8	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
176	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
177	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
178	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
180	M₁₆	—	4	2	no	—
181	M₁₆	—	4	2	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	4	1	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	8	4	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	2	2	no	—
193	C₄²	—	4	1	no	—
194	C₄²	—	4	1	no	—
195	C₄²	C₂×D₄×C₆₁	1	2	yes	—
196	C₄²	#41×C₆₁	1	2	yes	—
197	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
198	Q₈	—	4	2	no	—
199	Q₈	—	4	2	no	—
200	Q₈	—	8	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
214	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
215	C₂×C₄	#121×C₆₁	1	2	yes	—
216	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
217	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
218	C₂×C₄	#137×C₆₁	1	2	yes	—
219	C₂×C₄	#137×C₆₁	1	1	yes	characteristic
220	C₈	—	4	4	no	—
221	C₈	—	8	2	no	—
222	C₂²	—	2	1	no	—
223	C₂²	—	2	1	no	—
224	C₂²	C₆₁×#386	1	1	yes	characteristic
225	C₂²	C₆₁×#417	1	1	yes	characteristic
226	C₂²	C₆₁×#419	1	1	yes	characteristic
227	C₄	—	2	1	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	4	no	—
230	C₄	—	4	2	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	C₆₁×#456	1	2	yes	—
234	C₄	C₆₁×#468	1	2	yes	—
235	C₄	C₆₁×#470	1	2	yes	—
236	C₂	—	2	1	no	—
237	C₂	—	2	1	no	—
238	C₂	C₆₁×#1886	1	1	yes	characteristic
239	C₂	C₆₁×#1894	1	1	yes	characteristic
240	C₂	C₆₁×#1914	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₆₁×#2983

C₂

yes

maximal, characteristic

C₆₁×#2567

C₂

yes

maximal, characteristic

C₆₁×#1801

C₂

yes

maximal, characteristic

C₆₁×#1548

C₂

yes

maximal

C₆₁×#1303

C₂

yes

maximal

C₂×C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×Q₈×C₆₁

C₂²

yes

characteristic

C₆₁×#446

—

C₆₁×#432

—

C₆₁×#431

C₂²

yes

—

C₆₁×#423

C₂²

yes

—

C₂×#101×C₆₁

—

C₆₁×#395

C₄

yes

—

C₆₁×#391

—

C₆₁×#389

—

C₆₁×#384

—

C₄×C₄⋊C₄×C₆₁

C₂²

yes

characteristic

C₆₁×#343

—

C₆₁×#333

—

C₂²×Q₈×C₆₁

C₂×C₄

yes

—

C₂²×Q₈×C₆₁

D₄

yes

characteristic

C₂×M₁₆×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

D₄

yes

—

#101×C₆₁

—

C₂²⋊C₈×C₆₁

—

#97×C₆₁

—

C₄×C₈×C₆₁

—

#95×C₆₁

—

#95×C₆₁

C₂×C₄

yes

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

C₂×D₄

yes

—

C₄²×C₆₁

#41

yes

—

C₂³×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₆₁

—

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×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄×D₄

yes

—

C₂×C₄×C₆₁

#120

yes

characteristic

C₂×C₄×C₆₁

#121

yes

—

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

—

C₂×C₄×C₆₁

#137

yes

characteristic

C₈×C₆₁

—

100

C₈×C₆₁

—

101

#9400

C₆₁

yes

maximal, characteristic, direct product factor, Sylow

102

C₂²×C₆₁

—

103

C₂²×C₆₁

—

104

C₂²×C₆₁

#386

yes

characteristic

105

C₂²×C₆₁

#417

yes

characteristic

106

C₂²×C₆₁

#419

yes

characteristic

107

C₄×C₆₁

—

108

C₄×C₆₁

—

109

C₄×C₆₁

—

110

C₄×C₆₁

—

111

C₄×C₆₁

—

112

C₄×C₆₁

—

113

C₄×C₆₁

#456

yes

—

114

C₄×C₆₁

#468

yes

—

115

C₄×C₆₁

#470

yes

—

116

#2983

C₂×C₆₁

yes

characteristic

117

#2567

C₂×C₆₁

yes

characteristic

118

#1801

C₂×C₆₁

yes

characteristic

119

#1548

C₂×C₆₁

yes

—

120

#1303

C₂×C₆₁

yes

—

121

C₂×C₆₁

—

122

C₂×C₆₁

—

123

C₂×C₆₁

#1886

yes

characteristic

124

C₂×C₆₁

#1894

yes

characteristic

125

C₂×C₆₁

#1914

yes

characteristic

126

C₂×C₄⋊Q₈

C₂²×C₆₁

yes

characteristic

127

C₂×C₄×Q₈

C₂²×C₆₁

yes

characteristic

128

#446

—

129

#432

—

130

#431

C₂²×C₆₁

yes

—

131

#423

C₂²×C₆₁

yes

—

132

C₂×#101

—

133

#395

C₄×C₆₁

yes

—

134

#391

—

135

#389

—

136

#384

—

137

C₄×C₄⋊C₄

C₂²×C₆₁

yes

characteristic

138

#343

—

139

#333

—

140

C₆₁

#9400

yes

characteristic, direct product factor, Sylow

141

C₂²×Q₈

C₂×C₄×C₆₁

yes

—

142

C₂²×Q₈

D₄×C₆₁

yes

characteristic

143

C₂×M₁₆

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

C₂×C₄×C₆₁

yes

—

153

C₂×C₄⋊C₄

D₄×C₆₁

yes

characteristic

154

C₂×C₄²

—

155

C₂×C₄²

D₄×C₆₁

yes

—

156

C₂×C₄²

C₂³×C₆₁

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

C₄⋊C₈

D₄×C₆₁

yes

—

161

#101

—

162

C₂²⋊C₈

—

163

#97

—

164

C₄×C₈

—

165

#95

—

166

#95

C₂×C₄×C₆₁

yes

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊C₄×C₆₁

yes

—

176

C₂²×C₄

C₂²⋊C₄×C₆₁

yes

—

177

C₂²×C₄

C₂²×C₄×C₆₁

yes

characteristic

178

C₂²×C₄

C₂×D₄×C₆₁

yes

characteristic

179

C₂²×C₄

C₂×D₄×C₆₁

yes

characteristic

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₄²

C₂×D₄×C₆₁

yes

—

196

C₄²

#41×C₆₁

yes

—

197

C₂³

C₂×C₂²⋊C₄×C₆₁

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

C₄×D₄×C₆₁

yes

—

214

C₂×C₄

#120×C₆₁

yes

characteristic

215

C₂×C₄

#121×C₆₁

yes

—

216

C₂×C₄

#123×C₆₁

yes

characteristic

217

C₂×C₄

AGL(1,ℤ/8)×C₆₁

yes

characteristic

218

C₂×C₄

#137×C₆₁

yes

—

219

C₂×C₄

#137×C₆₁

yes

characteristic

220

C₈

—

221

C₈

—

222

C₂²

—

223

C₂²

—

224

C₂²

C₆₁×#386

yes

characteristic

225

C₂²

C₆₁×#417

yes

characteristic

226

C₂²

C₆₁×#419

yes

characteristic

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

C₆₁×#456

yes

—

234

C₄

C₆₁×#468

yes

—

235

C₄

C₆₁×#470

yes

—

236

C₂

—

237

C₂

—

238

C₂

C₆₁×#1886

yes

characteristic

239

C₂

C₆₁×#1894

yes

characteristic

240

C₂

C₆₁×#1914

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₂³×C₆₁	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₆₁

#386

commutator

C₂²×C₄

C₂²×C₄×C₆₁

Frattini, cosocle

C₂×C₄²

C₂³×C₆₁

prime radical

C₂³×C₆₁

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

N	H ≅ G/N	type
101. #9400	C₆₁	direct (N × H)
140. C₆₁	#9400	direct (N × H)

H ≅ G/N

type

101. #9400

C₆₁

direct (N × H)

140. C₆₁

#9400

direct (N × H)

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

subgroup	index
C₆₁×#2983	2
C₆₁×#2567	2
C₆₁×#1801	2
C₆₁×#1548	2
C₆₁×#1303	2
#9400	61

subgroup

index

C₆₁×#2983

C₆₁×#2567

C₆₁×#1801

C₆₁×#1548

C₆₁×#1303

#9400

Subgroups — C₆₁×#9400 #29512833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C61×#9400 #29512833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#9400 #29512833