Finite Group Databasebeta

← C61×#19745 #29523178

Subgroups — C61×#19745 #29523178

Order 15616.

994 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3184C213yesmaximal, complemented
2C61×#3151C213yesmaximal, complemented
3C61×#1721C213yesmaximal, complemented
4C61×#1715C213yesmaximal, complemented
5C61×#1712C211yesmaximal, characteristic, complemented
6C61×#1705C211yesmaximal, characteristic, complemented
7C61×#1455C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C61—26no—
9C61×#532C2213yes—
10C2×#127×C61C2211yescharacteristic
11C61×#498C2213yescomplemented
12C61×#496—26no—
13C61×#493C2213yes—
14C61×#493C2213yes—
15C61×#493C2213yescomplemented
16C61×#492C2213yes—
17C61×#492C2213yes—
18C61×#486C2216yescomplemented
19C61×#469—26no—
20C61×#442—26no—
21C4×M16×C61C2213yes—
22C61×#322C2213yescomplemented
23C82×C61C2211yescharacteristic, complemented
24C2×#41×C61—23no—
25C22×D4×C61—23no—
26AGL(1,ℤ/8)×C61—424no—
27C2×SD16×C61—26no—
28C2×SD16×C61—26no—
29C2×D8×C61—26no—
30C2×D8×C61—26no—
31C2×D8×C61—26no—
32C2×M16×C61D416yes—
33C4⋊Q8×C61C2313yes—
34#127×C61—23no—
35#127×C61C2311yescharacteristic
36#127×C61C2311yescharacteristic
37#127×C61C2313yes—
38#124×C61—23no—
39#121×C61—26no—
40C4×D4×C61—26no—
41C2×C42×C61C2311yescharacteristic
42#106×C61—26no—
43#102×C61—212no—
44#97×C61D416yes—
45C4×C8×C61C2313yes—
46C4×C8×C61C2313yes—
47C24×C61—41no—
48#41×C61—412no—
49C2×Q8×C61—23no—
50C2×D4×C61—26no—
51C2×D4×C61—23no—
52C2×D4×C61—23no—
53C2×D4×C61—23no—
54C2×D4×C61—412no—
55C2×D4×C61—43no—
56C2×D4×C61—43no—
57C22×C4×C61—43no—
58C22×C4×C61C2×D413yes—
59SD16×C61—412no—
60SD16×C61—412no—
61D8×C61—412no—
62D8×C61—412no—
63D8×C61—412no—
64M16×C61—212no—
65C2×C8×C61C2×D416yes—
66C2×C8×C61C2×D416yes—
67C4⋊C4×C61—26no—
68C22⋊C4×C61—46no—
69C42×C61C2×D413yes—
70C42×C61C2411yescharacteristic
71C23×C61—43no—
72C23×C61—41no—
73C23×C61—41no—
74C23×C61—86no—
75C23×C61#12711yescharacteristic
76Q8×C61—46no—
77D4×C61—46no—
78D4×C61—46no—
79D4×C61—46no—
80D4×C61—412no—
81D4×C61—86no—
82D4×C61—86no—
83C2×C4×C61—26no—
84C2×C4×C61—43no—
85C2×C4×C61—86no—
86C2×C4×C61#12713yes—
87C2×C4×C61C22×D413yes—
88C8×C61—26no—
89C8×C61AGL(1,ℤ/8)112yescomplemented
90#19745C6111yesmaximal, characteristic, direct product factor, Sylow
91C22×C61—23no—
92C22×C61—83no—
93C22×C61—83no—
94C22×C61—83no—
95C22×C61—86no—
96C22×C61—164no—
97C22×C61C2×#12711yescharacteristic
98C4×C61—23no—
99C4×C61—83no—
100C4×C61C2×AGL(1,ℤ/8)16yes—
101#3184C2×C6113yescomplemented
102#3151C2×C6113yescomplemented
103#1721C2×C6113yescomplemented
104#1715C2×C6113yescomplemented
105#1712C2×C6111yescharacteristic, complemented
106#1705C2×C6111yescharacteristic, complemented
107#1455C2×C6111yescharacteristic, complemented
108C2×C61—41no—
109C2×C61—163no—
110C2×C61—161no—
111C2×C61—161no—
112C2×C61#315113yes—
113C2×AGL(1,ℤ/8)—26no—
114#532C22×C6113yes—
115C2×#127C22×C6111yescharacteristic
116#498C22×C6113yescomplemented
117#496—26no—
118#493C22×C6113yes—
119#493C22×C6113yes—
120#493C22×C6113yescomplemented
121#492C22×C6113yes—
122#492C22×C6113yes—
123#486C22×C6116yescomplemented
124#469—26no—
125#442—26no—
126C4×M16C22×C6113yes—
127#322C22×C6113yescomplemented
128C82C22×C6111yescharacteristic, complemented
129C61#1974511yescharacteristic, direct product factor, Sylow
130C2×#41—23no—
131C22×D4—23no—
132AGL(1,ℤ/8)—424no—
133C2×SD16—26no—
134C2×SD16—26no—
135C2×D8—26no—
136C2×D8—26no—
137C2×D8—26no—
138C2×M16D4×C6116yes—
139C4⋊Q8C23×C6113yes—
140#127—23no—
141#127C23×C6111yescharacteristic
142#127C23×C6111yescharacteristic
143#127C23×C6113yes—
144#124—23no—
145#121—26no—
146C4×D4—26no—
147C2×C42C23×C6111yescharacteristic
148#106—26no—
149#102—212no—
150#97D4×C6116yes—
151C4×C8C23×C6113yes—
152C4×C8C23×C6113yes—
153C24—41no—
154#41—412no—
155C2×Q8—23no—
156C2×D4—26no—
157C2×D4—23no—
158C2×D4—23no—
159C2×D4—23no—
160C2×D4—412no—
161C2×D4—43no—
162C2×D4—43no—
163C22×C4—43no—
164C22×C4C2×D4×C6113yes—
165SD16—412no—
166SD16—412no—
167D8—412no—
168D8—412no—
169D8—412no—
170M16—212no—
171C2×C8C2×D4×C6116yes—
172C2×C8C2×D4×C6116yes—
173C4⋊C4—26no—
174C22⋊C4—46no—
175C42C2×D4×C6113yes—
176C42C24×C6111yescharacteristic
177C23—43no—
178C23—41no—
179C23—41no—
180C23—86no—
181C23#127×C6111yescharacteristic
182Q8—46no—
183D4—46no—
184D4—46no—
185D4—46no—
186D4—412no—
187D4—86no—
188D4—86no—
189C2×C4—26no—
190C2×C4—43no—
191C2×C4—86no—
192C2×C4#127×C6113yes—
193C2×C4C22×D4×C6113yes—
194C8—26no—
195C8AGL(1,ℤ/8)×C61112yescomplemented
196C22—23no—
197C22—83no—
198C22—83no—
199C22—83no—
200C22—86no—
201C22—164no—
202C22C2×#127×C6111yescharacteristic
203C4—23no—
204C4—83no—
205C4C2×AGL(1,ℤ/8)×C6116yes—
206C2—41no—
207C2—161no—
208C2—161no—
209C2—163no—
210C2C61×#315113yes—
subgroupG/H
center, socleC22×C61C2×#127
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C61×#3184C2semidirect
2. C61×#3151C2semidirect
3. C61×#1721C2semidirect
4. C61×#1715C2semidirect
5. C61×#1712C2semidirect
6. C61×#1705C2semidirect
7. C61×#1455C2semidirect
11. C61×#498C22semidirect
15. C61×#493C22semidirect
18. C61×#486C22semidirect
22. C61×#322C22semidirect
23. C82×C61C22semidirect
89. C8×C61AGL(1,ℤ/8)semidirect
90. #19745C61direct (N × H)
101. #3184C2×C61semidirect
102. #3151C2×C61semidirect
103. #1721C2×C61semidirect
104. #1715C2×C61semidirect
105. #1712C2×C61semidirect
106. #1705C2×C61semidirect
107. #1455C2×C61semidirect
116. #498C22×C61semidirect
120. #493C22×C61semidirect
123. #486C22×C61semidirect
127. #322C22×C61semidirect
128. C82C22×C61semidirect
129. C61#19745direct (N × H)
195. C8AGL(1,ℤ/8)×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#31842
C61×#31512
C61×#17212
C61×#17152
C61×#17122
C61×#17052
C61×#14552
#1974561