Finite Group Databasebeta

← #29567642

Subgroups — #29567642

Order 15616.

198 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 41 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#21447164C211yesmaximal, characteristic
2#21443765C211yesmaximal, characteristic
3C61×#1296C211yesmaximal, characteristic
4#16840393C411yescharacteristic
5#16839802—21no—
6#16839531C411yescharacteristic
7#16839522—21no—
8#16839488—21no—
9C2×C4⋊C8×C61—21no—
10C61×#384C2211yescharacteristic
11C2×#11758194—21no—
12#14519776—41no—
13#14519768—41no—
14#14519756—41no—
15#14519736—21no—
16#14519710—41no—
17#14519708—41no—
18C22⋊#92418—41no—
19C22×C8×C61—41no—
20C2×C4⋊C4×C61—41no—
21C2×C4⋊C4×C61C2×C411yescharacteristic
22C2×C4⋊C4×C61D411yescharacteristic
23C2×C42×C61D411yescharacteristic
24C4⋊C8×C61—22no—
25C4⋊C8×C61—41no—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×Dic122—41no—
31C2×C8×C61—42no—
32C2×C8×C61—81no—
33C2×C8×C61—81no—
34C4⋊C4×C61—41no—
35C4⋊C4×C61—41no—
36C4⋊C4×C61—81no—
37C4⋊C4×C61—81no—
38C42×C61—21no—
39C42×C61SD1611yescharacteristic
40C42×C61Q1611yescharacteristic
41C22⋊Dic61—41no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—41no—
45#11758196—42no—
46C4×Dic61—41no—
47#11758194—22no—
48#11758194—41no—
49C2×#92418—41no—
50C2×#92418—81no—
51C23×C61#9911yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—81no—
63C2×C4×C61—81no—
64C2×C4×C61#10311yescharacteristic
65C2×C4×C61#10411yescharacteristic
66C2×Dic61—41no—
67C2×Dic61—41no—
68Dic122—161no—
69C8×C61—82no—
70#92418—42no—
71#92418—161no—
72#7443—611nomaximal, Sylow
73C22×C61—21no—
74C22×C61—21no—
75C22×C61#32811yescharacteristic
76C22×C61AΣL(1,𝔽16)11yescharacteristic
77C22×C61#35611yescharacteristic
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—21no—
84C4×C61—81no—
85C4×C61—81no—
86Dic61—81no—
87Dic61—81no—
88#2060—611no—
89#1325—611no—
90#1296D6111yescharacteristic
91C2×C61—21no—
92C2×C61—21no—
93C2×C61#135411yescharacteristic
94C2×C61#140211yescharacteristic
95C2×C61#140511yescharacteristic
96#544—611no—
97#428—1221no—
98C2×C4⋊C8—21no—
99#384C2×D6111yescharacteristic
100#343—611no—
101#339—1221no—
102#324—1221no—
103C61#744311yescharacteristic, complemented, Sylow
104C2×M16—1221no—
105C22×C8—41no—
106C4⋊Q8—2441no—
107#125—2441no—
108C22⋊Q8—2441no—
109#117—1221no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C4×D6111yescharacteristic
112C2×C4⋊C4D24411yescharacteristic
113C2×C42C22⋊D6111yescharacteristic
114#107—2441no—
115#106—2441no—
116C4⋊C8—22no—
117C4⋊C8—41no—
118C22⋊C8—2441no—
119C2×Q8—2441no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4#1175819811yescharacteristic
124M16—1222no—
125M16—2441no—
126C2×C8—42no—
127C2×C8—81no—
128C2×C8—81no—
129C2×C8—4881no—
130C2×C8—2441no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—2441no—
138C4⋊C4—2442no—
139C22⋊C4—2441no—
140C42—21no—
141C42—2441no—
142C42#1175820011yescharacteristic
143C42#1175820211yescharacteristic
144C23#1451969111yescharacteristic
145Q8—9761no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4#1451970011yescharacteristic
161C2×C4#1451970511yescharacteristic
162C8—82no—
163C8—9761no—
164C8—2442no—
165C22—21no—
166C22—21no—
167C22#1683949811yescharacteristic
168C22#1683955011yescharacteristic
169C22#1683956011yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—4881no—
179C4—4881no—
180C2—21no—
181C2—21no—
182C2#2144384811yescharacteristic
183C2#2144396511yescharacteristic
184C2#2144397411yescharacteristic
subgroupG/H
centerC22#16839550
commutatorC2×C4⋊C4×C61C2×C4
Frattini#384C2×D61
FittingC61×#1296C2
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocleC61×#384C22
hypercenter#1296D61
hypocenterC61#7443
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1296

Complements

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

NH ≅ G/Ntype
103. C61#7443semidirect

Maximal subgroups

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

subgroupindex
#214471642
#214437652
C61×#12962
#744361