Finite Group Databasebeta

← #30595037

Subgroups — #30595037

Order 15616.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460760C211yesmaximal, characteristic
2#21460695C211yesmaximal, characteristic
3#21447166C211yesmaximal, characteristic
4C2×#14519832—21no—
5#16840607—21no—
6#16839805—21no—
7#16839627C2211yescharacteristic
8#16839531C411yescharacteristic
9#16839521—21no—
10C61×#544C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13#14519832—22no—
14#14519832—41no—
15C2×#11758194—21no—
16C2×C4⋊Dic61D411yescharacteristic
17C2×C4×Dic61D411yescharacteristic
18#14519710—41no—
19#14519708—41no—
20#14519684—41no—
21C4⋊Q8×C61—41no—
22#125×C61—41no—
23C22⋊Q8×C61—41no—
24#117×C61—21no—
25C2×C4⋊C4×C61C2×C411yescharacteristic
26C2×Q8×C61—41no—
27C22×C4×C61—21no—
28C22×C4×C61C22⋊C411yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C2×#92420—42no—
32C2×#92420—42no—
33C2×#92420—42no—
34C2×#92420—81no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—41no—
38C4⋊C4×C61—42no—
39C4⋊C4×C61—41no—
40C22⋊C4×C61—41no—
41C42×C61—41no—
42C4⋊Dic61—41no—
43C4×Dic61—21no—
44C4×Dic61SD1611yescharacteristic
45C4×Dic61Q1611yescharacteristic
46#11758194—22no—
47#11758194—41no—
48C2×#92418—41no—
49C23×C61#9911yescharacteristic
50Q8×C61—161no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—81no—
57C2×C4×C61#10311yescharacteristic
58C2×C4×C61#10411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—41no—
64C2×Dic61—81no—
65#92420—44no—
66#92420—161no—
67#92418—42no—
68#7442—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#32811yescharacteristic
72C22×C61AΣL(1,𝔽16)11yescharacteristic
73C22×C61#35611yescharacteristic
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—81no—
77C4×C61—81no—
78C4×C61—81no—
79Dic61—41no—
80Dic61—41no—
81Dic61—81no—
82#2061—611no—
83#1324—611no—
84#1295—611no—
85C2×C61—21no—
86C2×C61—21no—
87C2×C61#135411yescharacteristic
88C2×C61#140311yescharacteristic
89C2×C61#140411yescharacteristic
90#544#692311yescharacteristic
91#428—1221no—
92C2×#97—1221no—
93#382—611no—
94#343—611no—
95#339—1221no—
96#324—1221no—
97C61#744211yescharacteristic, complemented, Sylow
98C2×M16—1221no—
99C22×C8—2441no—
100C4⋊Q8—41no—
101#125—41no—
102C22⋊Q8—41no—
103#117—21no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4C2×#692311yescharacteristic
106C2×C42—611no—
107#107—2441no—
108#106—2441no—
109C22⋊C8—2441no—
110#97—1222no—
111#97—2441no—
112#95—2441no—
113C2×Q8—41no—
114C22×C4—21no—
115C22×C4—1221no—
116C22×C4—1221no—
117C22×C4C22⋊#692311yescharacteristic
118M16—1222no—
119M16—2441no—
120C2×C8—4881no—
121C2×C8—2441no—
122C2×C8—2442no—
123C2×C8—2442no—
124C2×C8—2442no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—41no—
128C4⋊C4—41no—
129C4⋊C4—42no—
130C4⋊C4—2441no—
131C22⋊C4—41no—
132C42—41no—
133C42—611no—
134C42—611no—
135C42—1221no—
136C23#1451983511yescharacteristic
137Q8—161no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—1221no—
145C2×C4—1221no—
146C2×C4—4881no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4—2441no—
150C2×C4#1451984011yescharacteristic
151C2×C4#1451984211yescharacteristic
152C8—9761no—
153C8—2442no—
154C8—2444no—
155C22—21no—
156C22—21no—
157C22#1684061611yescharacteristic
158C22#1684066211yescharacteristic
159C22#1684067211yescharacteristic
160C4—21no—
161C4—21no—
162C4—81no—
163C4—81no—
164C4—81no—
165C4—4881no—
166C4—2441no—
167C4—2441no—
168C2—21no—
169C2—21no—
170C2#2146082011yescharacteristic
171C2#2146094011yescharacteristic
172C2#2146094211yescharacteristic
subgroupG/H
centerC22#16840662
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#544C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocle#16839627C22
hypercenter#544#6923
hypocenterC61#7442
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #544

Complements

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

NH ≅ G/Ntype
97. C61#7442semidirect

Maximal subgroups

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

subgroupindex
#214607602
#214606952
#214471662
#744261