Finite Group Databasebeta

← #29567558

Subgroups — #29567558

Order 15616.

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

normal subgroups only

This group has 190 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#21447106C211yesmaximal, characteristic
2#21443770C211yesmaximal, characteristic, complemented
3C61×#1307C211yesmaximal, characteristic, complemented
4#16840562C411yescharacteristic
5C2×#14519705—21no—
6#16839744—21no—
7#16839544—21no—
8#16839520C411yescharacteristic
9C61×#432—21no—
10C61×#423C2211yescharacteristic
11C2×#11758222—21no—
12#14519810—41no—
13#14519805—41no—
14#14519799—41no—
15C2×#11758194—21no—
16#14519717—41no—
17#14519705—41no—
18#14519705—41no—
19#14519695—41no—
20#14519693—41no—
21C2×M16×C61C2×C411yescharacteristic
22C2×M16×C61D411yescharacteristic
23C2×C42×C61D411yescharacteristic
24C4⋊C8×C61—41no—
25C4⋊C8×C61—41no—
26C22⋊C8×C61—22no—
27#97×C61—41no—
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×C22⋊D61—41no—
31#11758222—41no—
32#11758222—41no—
33#11758222—41no—
34#11758222—41no—
35C2×D244—21no—
36C2×C4×D61—41no—
37C2×Dic122—21no—
38M16×C61—41no—
39M16×C61—41no—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C2×C8×C61—42no—
43C42×C61—21no—
44C42×C61D811yescharacteristic
45C42×C61SD1611yescharacteristic
46#11758194—41no—
47#11758194—41no—
48C2×#92418—41no—
49Dic244—41no—
50D488—41no—
51#11758190—42no—
52#11758185—81no—
53C23×C61#10411yescharacteristic
54C22×D61—41no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—81no—
60C2×C4×C61#9911yescharacteristic
61C2×C4×C61#10211yescharacteristic
62C22⋊D61—81no—
63C22⋊D61—81no—
64C2×Dic61—41no—
65D244—41no—
66D244—41no—
67C4×D61—81no—
68C4×D61—81no—
69Dic122—41no—
70Dic122—41no—
71C8×C61—41no—
72C8×C61—41no—
73C8×C61—82no—
74#92418—81no—
75#7415—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—41no—
78C22×C61#32711yescharacteristic
79C2×D61—81no—
80C2×D61—161no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84C4×C61AΣL(1,𝔽16)11yescharacteristic
85C4×C61#35511yescharacteristic
86Dic61—81no—
87#2050—611no—
88#1327—611no—
89#1307D6111yescharacteristic, complemented
90C2×C61—21no—
91C2×C61—41no—
92C2×C61#134511yescharacteristic
93D61—161no—
94#575—611no—
95#432—21no—
96#423C2×D6111yescharacteristic
97C2×#104—1221no—
98#413—1221no—
99#349—1221no—
100#338—611no—
101C61#741511yescharacteristic, complemented, Sylow
102C2×#41—1221no—
103#137—2441no—
104AGL(1,ℤ/8)—2441no—
105#135—2441no—
106C2×M16—1221no—
107C2×M16C4×D6111yescharacteristic
108C2×M16D24411yescharacteristic
109C2×C42C22⋊D6111yescharacteristic
110M32—2441no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113#104—2441no—
114#104—2441no—
115#101—2441no—
116#100—2441no—
117C22⋊C8—22no—
118#97—41no—
119#41—2441no—
120#41—2441no—
121#41—2441no—
122#41—2441no—
123C2×Q8—1221no—
124C2×D4—1221no—
125C2×D4—2441no—
126C22×C4—21no—
127C22×C4—2441no—
128C22×C4#1175819811yescharacteristic
129Q16—2441no—
130SD16—2442no—
131D8—2441no—
132M16—41no—
133M16—41no—
134M16—2441no—
135M16—2441no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—42no—
139C2×C8—2441no—
140C42—21no—
141C42#1175819911yescharacteristic
142C42#1175820111yescharacteristic
143C16—4881no—
144C23—2441no—
145C23#1451970511yescharacteristic
146Q8—2441no—
147Q8—2441no—
148D4—4881no—
149D4—4881no—
150D4—2441no—
151D4—2441no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—81no—
157C2×C4—4881no—
158C2×C4—4881no—
159C2×C4—2441no—
160C2×C4#1451969111yescharacteristic
161C2×C4#1451969711yescharacteristic
162C8—41no—
163C8—41no—
164C8—82no—
165C8—4881no—
166C22—21no—
167C22—41no—
168C22—9761no—
169C22—4881no—
170C22#1683949511yescharacteristic
171C4—21no—
172C4—41no—
173C4—41no—
174C4—4881no—
175C4#1683955011yescharacteristic
176C4#1683955811yescharacteristic
177C2—21no—
178C2—41no—
179C2—9761no—
180C2#2144382111yescharacteristic
subgroupG/H
centerC2#21443821
commutatorC2×M16×C61C2×C4
Frattini#423C2×D61
FittingC61×#1307C2
socleC2×C61#1345
prime radical#16840562C4
cosocleC61×#423C22
hypercenter#1307D61
hypocenterC61#7415
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #21443770C2semidirect
3. C61×#1307C2semidirect
89. #1307D61semidirect
101. C61#7415semidirect

Maximal subgroups

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

subgroupindex
#214471062
#214437702
C61×#13072
#741561