Finite Group Databasebeta

← #29593393

Subgroups — #29593393

Order 15616.

274 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#21457213C211yesmaximal, characteristic
2#21448038C212yesmaximal
3#21443806C212yesmaximal
4#21443770C211yesmaximal, characteristic
5C61×#2102C211yesmaximal, characteristic
6#16840319—21no—
7#16840048—22no—
8#16840020—21no—
9#16840020C2212yes—
10#16839973—22no—
11#16839586—22no—
12#16839577—22no—
13#16839544C2212yes—
14C61×#430C2211yescharacteristic
15C61×#423C2211yescharacteristic
16C61×#344—21no—
17C61×#339—21no—
18C61×H(3,ℤ/4)C2211yescharacteristic
19C2×Dic244—21no—
20C2×Dic244D412yes—
21#14519777—21no—
22#14519777—21no—
23#14519769—41no—
24#14519756—22no—
25#14519756—41no—
26C4×Dic122—22no—
27C4×Dic122—41no—
28#14519736—41no—
29#14519717—22no—
30#14519709—21no—
31#14519709D412yes—
32#14519702—22no—
33#14519702—22no—
34C2×M16×C61—21no—
35C2×M16×C61D411yescharacteristic
36C2×M16×C61C2311yescharacteristic
37#117×C61—21no—
38C2×C42×C61D411yescharacteristic
39#108×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61—21no—
42C22×C4×C61C2×D411yescharacteristic
43C2×Dic122—22no—
44C2×Dic122—41no—
45M16×C61—41no—
46M16×C61—41no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D412yes—
52C4⋊C4×C61—41no—
53C22⋊C4×C61—41no—
54C42×C61—21no—
55C42×C61—41no—
56C42×C61SD1611yescharacteristic
57C42×C61SD1611yescharacteristic
58C22⋊Dic61—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63#11758196—42no—
64#11758196—42no—
65C4×Dic61—42no—
66Dic244—42no—
67Dic244—81no—
68#11758185—42no—
69C23×C61AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61—81no—
76C2×C4×C61#12011yescharacteristic
77C2×C4×C61C2×SD1611yescharacteristic
78C2×Dic61—42no—
79C2×Dic61—42no—
80Dic122—42no—
81Dic122—42no—
82Dic122—82no—
83C8×C61—22no—
84C8×C61—41no—
85C8×C61—81no—
86#12308—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—41no—
89C22×C61#45011yescharacteristic
90C4×C61—22no—
91C4×C61—21no—
92C4×C61—41no—
93C4×C61—161no—
94C4×C61#45411yescharacteristic
95C4×C61#45811yescharacteristic
96Dic61—82no—
97Dic61—82no—
98#3255—611no—
99#2239—612no—
100#2102D6111yescharacteristic
101#1340—612no—
102#1327—611no—
103C2×C61—21no—
104C2×C61—41no—
105C2×C61#161611yescharacteristic
106#533—1221no—
107#475—1222no—
108#470—612no—
109#470—1221no—
110#462—1222no—
111#430C2×D6111yescharacteristic
112#423C2×D6111yescharacteristic
113#365—1222no—
114#362—1222no—
115#349—612no—
116#344—21no—
117#339—21no—
118H(3,ℤ/4)C2×D6111yescharacteristic
119C61#1230811yescharacteristic, complemented, Sylow
120C2×Q16—612no—
121C2×Q16—1221no—
122C2×M16—21no—
123C2×M16C22⋊D6111yescharacteristic
124C2×M16C22×D6111yescharacteristic
125C4⋊Q8—1221no—
126C4⋊Q8—1221no—
127#125—2441no—
128C22⋊Q8—1222no—
129C22⋊Q8—2441no—
130C4×Q8—1222no—
131C4×Q8—2441no—
132#117—21no—
133#117—2441no—
134C2×C42C22⋊D6111yescharacteristic
135M32—1222no—
136#108—22no—
137#106—612no—
138#106—1221no—
139C4⋊C8—22no—
140#103—1222no—
141#103—1222no—
142C2×Q8—1222no—
143C2×Q8—2441no—
144C22×C4—21no—
145C22×C4C2×C22⋊D6111yescharacteristic
146Q16—4881no—
147Q16—2442no—
148M16—41no—
149M16—41no—
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8D4×D6112yes—
155C4⋊C4—41no—
156C4⋊C4—1222no—
157C4⋊C4—2442no—
158C4⋊C4—2441no—
159C4⋊C4—2441no—
160C4⋊C4—2441no—
161C4⋊C4—2442no—
162C22⋊C4—41no—
163C22⋊C4—2442no—
164C42—21no—
165C42—41no—
166C42—2442no—
167C42#1175820111yescharacteristic
168C42#1175820111yescharacteristic
169C16—2442no—
170C23#1451980211yescharacteristic
171Q8—4882no—
172Q8—2442no—
173Q8—2442no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—81no—
180C2×C4—2442no—
181C2×C4—2442no—
182C2×C4#1451974511yescharacteristic
183C2×C4C2×#1175820111yescharacteristic
184C8—22no—
185C8—41no—
186C8—81no—
187C22—21no—
188C22—41no—
189C22#1683991211yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—161no—
194C4—4882no—
195C4—4882no—
196C4#1683993411yescharacteristic
197C4#1683995111yescharacteristic
198C2—21no—
199C2—41no—
200C2#2144485511yescharacteristic
subgroupG/H
centerC2#21444855
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#2102C2
socleC2×C61#1616
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#2102D61
hypocenterC61#12308
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2102

Complements

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

NH ≅ G/Ntype
119. C61#12308semidirect

Maximal subgroups

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

subgroupindex
#214572132
#214480382
#214438062
#214437702
C61×#21022
#1230861