Finite Group Databasebeta

← #29593394

Subgroups — #29593394

Order 15616.

274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448036C212yesmaximal
2#21447394C211yesmaximal, characteristic
3#21443807C212yesmaximal
4#21443770C211yesmaximal, characteristic
5C61×#3255C211yesmaximal, characteristic
6#16839811C2211yescharacteristic
7#16839584—22no—
8#16839578—22no—
9#16839544C2212yes—
10#16839534—21no—
11#16839522—21no—
12#16839519C2211yescharacteristic
13C61×#533—21no—
14C61×#475—22no—
15C61×#470—21no—
16C61×#470C2212yes—
17C61×#462—22no—
18C61×#423C2211yescharacteristic
19C2×#11758194—21no—
20#14519736—21no—
21#14519717—22no—
22#14519713—22no—
23C2×Q16×C61—21no—
24C2×Q16×C61D412yes—
25C2×M16×C61D411yescharacteristic
26C2×M16×C61C2311yescharacteristic
27C4⋊Q8×C61—21no—
28C4⋊Q8×C61—21no—
29#125×C61—41no—
30C22⋊Q8×C61—22no—
31C22⋊Q8×C61—41no—
32C4×Q8×C61—22no—
33C4×Q8×C61—41no—
34#117×C61—41no—
35C2×C42×C61D411yescharacteristic
36#106×C61—21no—
37#106×C61D412yes—
38C4⋊C8×C61—22no—
39#103×C61—22no—
40#103×C61—22no—
41C2×Q8×C61—22no—
42C2×Q8×C61—41no—
43C22×C4×C61—21no—
44C22×C4×C61C2×D411yescharacteristic
45Q16×C61—42no—
46Q16×C61—81no—
47M16×C61—41no—
48M16×C61—41no—
49C2×C8×C61—21no—
50C2×C8×C61C2×D412yes—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—41no—
53C4⋊C4×C61—41no—
54C4⋊C4×C61—42no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—42no—
57C22⋊C4×C61—42no—
58C42×C61—21no—
59C42×C61—42no—
60C42×C61SD1611yescharacteristic
61C42×C61SD1611yescharacteristic
62C22⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4×Dic61—41no—
65#11758194—41no—
66#11758194—41no—
67C2×#92418—41no—
68#11758185—42no—
69C23×C61AGL(1,ℤ/8)11yescharacteristic
70Q8×C61—42no—
71Q8×C61—42no—
72Q8×C61—82no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61#12011yescharacteristic
81C2×C4×C61C2×SD1611yescharacteristic
82C2×Dic61—81no—
83C8×C61—22no—
84C8×C61—41no—
85#92418—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—82no—
94C4×C61—82no—
95C4×C61#45411yescharacteristic
96C4×C61#45811yescharacteristic
97Dic61—161no—
98#3255D6111yescharacteristic
99#2239—612no—
100#2102—611no—
101#1340—612no—
102#1327—611no—
103C2×C61—21no—
104C2×C61—41no—
105C2×C61#161611yescharacteristic
106#533—21no—
107#475—22no—
108#470—21no—
109#470C2×D6112yes—
110#462—22no—
111#430—611no—
112#423C2×D6111yescharacteristic
113#365—1222no—
114#362—1222no—
115#349—612no—
116#344—1221no—
117#339—1221no—
118H(3,ℤ/4)—611no—
119C61#1230811yescharacteristic, complemented, Sylow
120C2×Q16—21no—
121C2×Q16C22⋊D6112yes—
122C2×M16—1221no—
123C2×M16C22⋊D6111yescharacteristic
124C2×M16C22×D6111yescharacteristic
125C4⋊Q8—21no—
126C4⋊Q8—21no—
127#125—41no—
128C22⋊Q8—22no—
129C22⋊Q8—41no—
130C4×Q8—22no—
131C4×Q8—41no—
132#117—41no—
133#117—1221no—
134C2×C42C22⋊D6111yescharacteristic
135M32—1222no—
136#108—1222no—
137#106—21no—
138#106C22⋊D6112yes—
139C4⋊C8—22no—
140#103—22no—
141#103—22no—
142C2×Q8—22no—
143C2×Q8—41no—
144C22×C4—21no—
145C22×C4C2×C22⋊D6111yescharacteristic
146Q16—42no—
147Q16—81no—
148M16—41no—
149M16—41no—
150M16—2441no—
151M16—2441no—
152C2×C8—21no—
153C2×C8—2441no—
154C2×C8C2×C22⋊D6112yes—
155C4⋊C4—22no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—42no—
161C4⋊C4—2441no—
162C22⋊C4—42no—
163C22⋊C4—2441no—
164C42—21no—
165C42—42no—
166C42—2441no—
167C42#1175820011yescharacteristic
168C42#1175820011yescharacteristic
169C16—2442no—
170C23#1451980311yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—4881no—
182C2×C4#1451974611yescharacteristic
183C2×C4C2×#1175820011yescharacteristic
184C8—22no—
185C8—41no—
186C8—4881no—
187C22—21no—
188C22—41no—
189C22#1683991311yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—9761no—
196C4#1683993511yescharacteristic
197C4#1683995211yescharacteristic
198C2—21no—
199C2—41no—
200C2#2144485611yescharacteristic
subgroupG/H
centerC2#21444856
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#3255C2
socleC2×C61#1616
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#3255D61
hypocenterC61#12308
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3255

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
#214480362
#214473942
#214438072
#214437702
C61×#32552
#1230861