Finite Group Databasebeta

← #29567509

Subgroups — #29567509

Order 15616.

258 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 37 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#21446928C211yesmaximal, characteristic
2#21443940C211yesmaximal, characteristic, complemented
3C61×#1321C211yesmaximal, characteristic, complemented
4C2×#14519802—21no—
5C22×D488C411yescharacteristic, complemented
6C2×#14519693—21no—
7#16839736—21no—
8#16839527C411yescharacteristic, complemented
9C61×#408C2211yescharacteristic
10C61×#349—21no—
11C22×D244—21no—
12#14519802—42no—
13#14519802—42no—
14C2×#11758201—41no—
15C2×D488—41no—
16C2×D488—42no—
17C2×#11758199—41no—
18C2×#11758194—21no—
19#14519736—41no—
20#14519693—42no—
21#14519692—22no—
22#14519692—41no—
23C2×#41×C61D411yescharacteristic
24C2×M16×C61D411yescharacteristic
25C22×C8×C61C2×C411yescharacteristic
26M32×C61—41no—
27C22⋊C8×C61—41no—
28C23×D61—41no—
29#41×C61—41no—
30#41×C61—41no—
31C2×Q8×C61SD1611yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61D811yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C22⋊C411yescharacteristic
36C2×D244—22no—
37C2×D244—41no—
38C2×D244—41no—
39C2×D244—41no—
40C2×D244—41no—
41C2×D244—41no—
42M16×C61—41no—
43C2×C8×C61—21no—
44C2×C8×C61—21no—
45C2×C8×C61—41no—
46C22⋊Dic61—42no—
47#11758201—44no—
48#11758199—44no—
49C4⋊Dic61—81no—
50C4×Dic61—81no—
51#11758194—22no—
52#11758194—41no—
53C2×#92418—41no—
54D488—42no—
55D488—42no—
56C16×C61—81no—
57C23×C61—21no—
58C23×C61#10411yescharacteristic
59C22×D61—42no—
60C22×D61—81no—
61C22×D61—81no—
62C22×D61—162no—
63Q8×C61—41no—
64D4×C61—41no—
65D4×C61—81no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61#9911yescharacteristic
72C2×C4×C61#10211yescharacteristic
73C2×Dic61—82no—
74D244—42no—
75D244—42no—
76D244—81no—
77D244—81no—
78C8×C61—41no—
79C8×C61—41no—
80#92418—42no—
81#7398—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—81no—
86C22×C61#32711yescharacteristic
87C2×D61—82no—
88C2×D61—162no—
89C2×D61—162no—
90C2×D61—162no—
91C4×C61—21no—
92C4×C61—41no—
93C4×C61AΣL(1,𝔽16)11yescharacteristic
94C4×C61#35311yescharacteristic
95Dic61—162no—
96#2018—611no—
97#1391—611no—
98#1321D6111yescharacteristic, complemented
99C2×C61—21no—
100C2×C61—41no—
101C2×C61—81no—
102C2×C61#134311yescharacteristic
103D61—162no—
104C2×AGL(1,ℤ/8)—1221no—
105C22×D8—611no—
106C2×#100—1221no—
107#410—1221no—
108#408C2×D6111yescharacteristic
109#349—21no—
110#341—611no—
111C61#739811yescharacteristic, complemented, Sylow
112C2×#41D24411yescharacteristic
113C22×D4—1221no—
114AGL(1,ℤ/8)—2442no—
115AGL(1,ℤ/8)—2442no—
116C2×SD16—2441no—
117C2×D8—2441no—
118C2×D8—2442no—
119C2×D8—2441no—
120C2×M16—1221no—
121C2×M16C22⋊D6111yescharacteristic
122C22×C8C4×D6111yescharacteristic
123#117—2441no—
124M32—41no—
125#100—2442no—
126#99—1222no—
127#99—2441no—
128C22⋊C8—41no—
129C24—2441no—
130#41—41no—
131#41—41no—
132C2×Q8#1175819011yescharacteristic
133C2×D4—21no—
134C2×D4—1222no—
135C2×D4—2441no—
136C2×D4—2441no—
137C2×D4—2441no—
138C2×D4—2441no—
139C2×D4—2441no—
140C2×D4D48811yescharacteristic
141C22×C4—21no—
142C22×C4#1175819811yescharacteristic
143SD16—2444no—
144D8—2442no—
145D8—2442no—
146D8—2444no—
147M16—41no—
148M16—1222no—
149M16—2441no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8—2441no—
154C4⋊C4—4881no—
155C22⋊C4—2442no—
156C42—4881no—
157C16—81no—
158C23—21no—
159C23—9762no—
160C23—4881no—
161C23—4881no—
162C23—2442no—
163C23#1451970311yescharacteristic
164Q8—41no—
165D4—41no—
166D4—81no—
167D4—4881no—
168D4—4881no—
169D4—2442no—
170D4—2442no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—4882no—
177C2×C4#1451969111yescharacteristic
178C2×C4#1451969911yescharacteristic
179C8—41no—
180C8—41no—
181C8—2442no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—81no—
186C22—9762no—
187C22—9762no—
188C22—9762no—
189C22—4882no—
190C22#1683949711yescharacteristic
191C4—21no—
192C4—41no—
193C4—9762no—
194C4#1683955011yescharacteristic
195C4#1683955411yescharacteristic
196C2—21no—
197C2—41no—
198C2—81no—
199C2—9762no—
200C2#2144381711yescharacteristic
subgroupG/H
centerC2#21443817
commutatorC22×C8×C61C2×C4
Frattini#408C2×D61
FittingC61×#1321C2
socleC2×C61#1343
prime radical#21446928C2
cosocleC61×#408C22
hypercenter#1321D61
hypocenterC61#7398
LCSG ▷ C22×C8×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #21443940C2semidirect
3. C61×#1321C2semidirect
5. C22×D488C4semidirect
8. #16839527C4semidirect
98. #1321D61semidirect
111. C61#7398semidirect

Maximal subgroups

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

subgroupindex
#214469282
#214439402
C61×#13212
#739861