Finite Group Databasebeta

← #29567515

Subgroups — #29567515

Order 15616.

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

normal subgroups only

This group has 254 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#21443942C211yesmaximal, characteristic, complemented
3C61×#1321C211yesmaximal, characteristic, complemented
4C2×#14519802—21no—
5C22×D488C411yescharacteristic
6#16839746—21no—
7C2×#14519693—21no—
8#16839527C411yescharacteristic
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—
19C2×#11758194—41no—
20#14519696—41no—
21#14519694—22no—
22#14519693—42no—
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×C61D811yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61SD1611yescharacteristic
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—
46#11758201—44no—
47#11758199—44no—
48#11758194—22no—
49#11758194—41no—
50#11758194—42no—
51#11758194—81no—
52C2×#92418—41no—
53C2×#92418—81no—
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
73D244—42no—
74D244—42no—
75D244—81no—
76D244—81no—
77C8×C61—41no—
78C8×C61—41no—
79#92418—42no—
80#92418—82no—
81#7400—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
95#2018—611no—
96#1392—611no—
97#1321D6111yescharacteristic, complemented
98C2×C61—21no—
99C2×C61—41no—
100C2×C61—81no—
101C2×C61#134311yescharacteristic
102D61—162no—
103C2×AGL(1,ℤ/8)—1221no—
104C22×D8—611no—
105#413—1221no—
106C2×#100—1221no—
107#408C2×D6111yescharacteristic
108#349—21no—
109#341—611no—
110C61#740011yescharacteristic, complemented, Sylow
111C2×#41D24411yescharacteristic
112C22×D4—1221no—
113AGL(1,ℤ/8)—2442no—
114AGL(1,ℤ/8)—2442no—
115C2×SD16—2441no—
116C2×D8—2441no—
117C2×D8—2442no—
118C2×D8—2441no—
119C2×M16—1221no—
120C2×M16—2441no—
121C2×M16C22⋊D6111yescharacteristic
122C22×C8C4×D6111yescharacteristic
123M32—41no—
124#101—2441no—
125#100—1222no—
126#100—2442no—
127C22⋊C8—41no—
128C24—2441no—
129#41—41no—
130#41—41no—
131C2×Q8D48811yescharacteristic
132C2×D4—21no—
133C2×D4—1222no—
134C2×D4—2441no—
135C2×D4—2441no—
136C2×D4—2441no—
137C2×D4—2441no—
138C2×D4—2441no—
139C2×D4#1175819011yescharacteristic
140C22×C4—21no—
141C22×C4#1175819811yescharacteristic
142SD16—2444no—
143D8—2442no—
144D8—2442no—
145D8—2444no—
146M16—41no—
147M16—1222no—
148M16—4881no—
149M16—2442no—
150M16—2441no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8—4881no—
155C2×C8—2441no—
156C16—81no—
157C23—21no—
158C23—9762no—
159C23—4881no—
160C23—4881no—
161C23—2442no—
162C23#1451970311yescharacteristic
163Q8—41no—
164D4—41no—
165D4—81no—
166D4—4881no—
167D4—4881no—
168D4—2442no—
169D4—2442no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4#1451969111yescharacteristic
176C2×C4#1451969911yescharacteristic
177C8—41no—
178C8—41no—
179C8—4882no—
180C8—2442no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22—9762no—
186C22—9762no—
187C22—9762no—
188C22—4882no—
189C22#1683949711yescharacteristic
190C4—21no—
191C4—41no—
192C4#1683955011yescharacteristic
193C4#1683955411yescharacteristic
194C2—21no—
195C2—41no—
196C2—81no—
197C2—9762no—
198C2#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#7400
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. #21443942C2semidirect
3. C61×#1321C2semidirect
97. #1321D61semidirect
110. C61#7400semidirect

Maximal subgroups

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

subgroupindex
#214469282
#214439422
C61×#13212
#740061