Finite Group Databasebeta

← #30594937

Subgroups — #30594937

Order 15616.

258 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 32 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#21460907C211yesmaximal, characteristic, complemented
2#21460754C211yesmaximal, characteristic, complemented
3#21446929C211yesmaximal, characteristic
4#16840741—21no—
5#16840658—21no—
6C2×#14519805—21no—
7C22×D488C411yescharacteristic, complemented
8C2×#14519693—21no—
9#16839728C2211yescharacteristic
10C61×#341C411yescharacteristic, complemented
11#14519856—41no—
12#14519851—41no—
13#14519836—41no—
14#14519835—22no—
15C2×#11758222D411yescharacteristic
16C22×D244—21no—
17#14519805—42no—
18#14519805—42no—
19C2×#11758190—41no—
20C2×D488—41no—
21C2×D488—41no—
22C2×D488—42no—
23C2×#11758194D411yescharacteristic
24#14519693—42no—
25#14519689—41no—
26C2×M16×C61—21no—
27C22×C8×C61C2×C411yescharacteristic
28C23×D61—41no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×C22⋊D61—21no—
31#11758222—41no—
32#11758222—41no—
33C2×D244—22no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—41no—
37C2×D244—41no—
38C2×D244—41no—
39C2×D244D811yescharacteristic
40C2×C4×D61—21no—
41C2×Dic122SD1611yescharacteristic
42C22⋊#6923—42no—
43C4⋊#6923—81no—
44C4×#6923—81no—
45M16×C61—22no—
46M16×C61—41no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50#11758194—41no—
51C2×#92418—21no—
52D488—42no—
53D488—44no—
54D488—42no—
55#11758190—44no—
56#11758187—81no—
57C23×C61#10411yescharacteristic
58C22×D61—21no—
59C22×D61—42no—
60C22×D61—81no—
61C22×D61—81no—
62C22×D61—162no—
63C2×#6923—82no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61#9911yescharacteristic
67C2×C4×C61#10211yescharacteristic
68C22⋊D61—81no—
69C2×Dic61—21no—
70D244—41no—
71D244—42no—
72D244—42no—
73D244—81no—
74D244—81no—
75C4×D61—41no—
76C4×D61—41no—
77Dic122—41no—
78C8×C61—42no—
79C8×C61—41no—
80#92418—41no—
81#7398—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—41no—
84C22×C61#32711yescharacteristic
85C2×D61—41no—
86C2×D61—81no—
87C2×D61—82no—
88C2×D61—162no—
89C2×D61—162no—
90C2×D61—162no—
91#6923—162no—
92C4×C61—21no—
93C4×C61AΣL(1,𝔽16)11yescharacteristic
94C4×C61#35311yescharacteristic
95Dic61—41no—
96#2018—611no—
97#1391—611no—
98#1321—611no—
99C2×C61—21no—
100C2×C61—41no—
101C2×C61#134311yescharacteristic
102D61—81no—
103D61—162no—
104C2×AGL(1,ℤ/8)—1221no—
105C22×D8—611no—
106C2×#100—1221no—
107#410—1221no—
108#408—611no—
109#349—1221no—
110#341#692311yescharacteristic, complemented
111C61#739811yescharacteristic, complemented, Sylow
112C2×#41—611no—
113C22×D4—1221no—
114AGL(1,ℤ/8)—2442no—
115AGL(1,ℤ/8)—2442no—
116C2×SD16—2441no—
117C2×D8—2441no—
118C2×D8—2441no—
119C2×D8—2442no—
120C2×M16—21no—
121C2×M16—611no—
122C22×C8C2×#692311yescharacteristic
123#117—2441no—
124M32—2441no—
125#100—2442no—
126#99—1222no—
127#99—2441no—
128C22⋊C8—2441no—
129C24—2441no—
130#41—2441no—
131#41—2441no—
132C2×Q8—611no—
133C2×D4—611no—
134C2×D4—1222no—
135C2×D4—1221no—
136C2×D4—2441no—
137C2×D4—2441no—
138C2×D4—2441no—
139C2×D4—2441no—
140C2×D4—2441no—
141C22×C4—1221no—
142C22×C4C22⋊#692311yescharacteristic
143SD16—2444no—
144D8—2442no—
145D8—2442no—
146D8—2444no—
147M16—22no—
148M16—41no—
149M16—2441no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—1221no—
154C4⋊C4—4881no—
155C22⋊C4—2442no—
156C42—4881no—
157C16—4881no—
158C23—1221no—
159C23—9762no—
160C23—4881no—
161C23—4881no—
162C23—2442no—
163C23#1451984211yescharacteristic
164Q8—2441no—
165D4—4881no—
166D4—4881no—
167D4—4881no—
168D4—2442no—
169D4—2441no—
170D4—2442no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—1221no—
174C2×C4—4882no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4#1451983611yescharacteristic
178C2×C4#1451983911yescharacteristic
179C8—42no—
180C8—41no—
181C8—2441no—
182C22—21no—
183C22—41no—
184C22—9762no—
185C22—9762no—
186C22—9762no—
187C22—4881no—
188C22—4882no—
189C22—2441no—
190C22#1684061411yescharacteristic
191C4—21no—
192C4—9762no—
193C4—2441no—
194C4#1684066311yescharacteristic
195C4#1684066711yescharacteristic
196C2—21no—
197C2—41no—
198C2—9762no—
199C2—4881no—
200C2#2146079811yescharacteristic
subgroupG/H
centerC2#21460798
commutatorC22×C8×C61C2×C4
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC2×C61#1343
prime radical#21446929C2
cosocle#16839728C22
hypercenter#341#6923
hypocenterC61#7398
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
1. #21460907C2semidirect
2. #21460754C2semidirect
7. C22×D488C4semidirect
10. C61×#341C4semidirect
110. #341#6923semidirect
111. C61#7398semidirect

Maximal subgroups

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

subgroupindex
#214609072
#214607542
#214469292
#739861