Finite Group Databasebeta

← #30594979

Subgroups — #30594979

Order 15616.

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

normal subgroups only

This group has 190 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#21460766C211yesmaximal, characteristic, complemented
2#21460725C211yesmaximal, characteristic, complemented
3#21447107C211yesmaximal, characteristic
4#16840783—21no—
5#16840658—21no—
6#16840562C411yescharacteristic
7#16839785C2211yescharacteristic
8C2×#14519703—21no—
9#16839744—21no—
10C61×#338C411yescharacteristic
11#14519851—41no—
12C4⋊#92420—41no—
13C22⋊#92420—22no—
14#14519832—41no—
15C2×#11758222—21no—
16#14519810—41no—
17#14519805—41no—
18#14519799—41no—
19C2×#11758194D411yescharacteristic
20C2×C4×Dic61D411yescharacteristic
21#14519706—41no—
22#14519703—41no—
23#14519703—41no—
24#14519695—41no—
25#14519693—41no—
26C2×M16×C61—21no—
27C2×M16×C61C2×C411yescharacteristic
28C22×C4×C61C22⋊C411yescharacteristic
29C2×C22⋊D61—41no—
30C22×Dic61—21no—
31#11758222—41no—
32#11758222—41no—
33#11758222—41no—
34#11758222—41no—
35C2×D244—21no—
36C2×C4×D61—41no—
37C2×Dic122—21no—
38C2×#92420—42no—
39M16×C61—41no—
40M16×C61—41no—
41M16×C61—41no—
42C2×C8×C61—21no—
43C2×C8×C61—41no—
44C4×Dic61—21no—
45C4×Dic61D811yescharacteristic
46C4×Dic61SD1611yescharacteristic
47#11758194—41no—
48C2×#92418—21no—
49Dic244—41no—
50D488—41no—
51#11758190—42no—
52#11758187—81no—
53C23×C61#10411yescharacteristic
54C22×D61—41no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61#9911yescharacteristic
58C2×C4×C61#10211yescharacteristic
59C22⋊D61—81no—
60C22⋊D61—81no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—41no—
64C2×Dic61—81no—
65D244—41no—
66D244—41no—
67C4×D61—81no—
68C4×D61—81no—
69Dic122—41no—
70Dic122—41no—
71#92420—82no—
72C8×C61—41no—
73C8×C61—81no—
74#92418—41no—
75#7415—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—41no—
78C22×C61#32711yescharacteristic
79C2×D61—81no—
80C2×D61—161no—
81C4×C61—21no—
82C4×C61AΣL(1,𝔽16)11yescharacteristic
83C4×C61#35511yescharacteristic
84Dic61—41no—
85Dic61—41no—
86Dic61—81no—
87#2050—611no—
88#1327—611no—
89#1307—611no—
90C2×C61—21no—
91C2×C61—41no—
92C2×C61#134511yescharacteristic
93D61—161no—
94#575—611no—
95#432—1221no—
96#423—611no—
97C2×#104—1221no—
98#413—1221no—
99#349—1221no—
100#338#692311yescharacteristic
101C61#741511yescharacteristic, complemented, Sylow
102C2×#41—1221no—
103#137—2441no—
104AGL(1,ℤ/8)—2441no—
105#135—2441no—
106C2×M16—21no—
107C2×M16—611no—
108C2×M16C2×#692311yescharacteristic
109C2×C42—611no—
110M32—2441no—
111C4⋊C8—2441no—
112C4⋊C8—2441no—
113#104—2441no—
114#104—2441no—
115#101—2441no—
116#100—2441no—
117C22⋊C8—1222no—
118#97—2441no—
119#41—2441no—
120#41—2441no—
121#41—2441no—
122#41—2441no—
123C2×Q8—1221no—
124C2×D4—1221no—
125C2×D4—2441no—
126C22×C4—1221no—
127C22×C4—2441no—
128C22×C4C22⋊#692311yescharacteristic
129Q16—2441no—
130SD16—2442no—
131D8—2441no—
132M16—41no—
133M16—41no—
134M16—41no—
135M16—2441no—
136C2×C8—21no—
137C2×C8—41no—
138C2×C8—1221no—
139C2×C8—2442no—
140C42—611no—
141C42—611no—
142C42—1221no—
143C16—4881no—
144C23—2441no—
145C23#1451984211yescharacteristic
146Q8—2441no—
147Q8—2441no—
148D4—4881no—
149D4—4881no—
150D4—2441no—
151D4—2441no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—4881no—
157C2×C4—4881no—
158C2×C4—4881no—
159C2×C4—2441no—
160C2×C4#1451983611yescharacteristic
161C2×C4#1451983911yescharacteristic
162C8—41no—
163C8—81no—
164C8—4882no—
165C8—2441no—
166C22—21no—
167C22—41no—
168C22—9761no—
169C22—4881no—
170C22#1684061411yescharacteristic
171C4—21no—
172C4—4881no—
173C4—2441no—
174C4—2441no—
175C4#1684066311yescharacteristic
176C4#1684067111yescharacteristic
177C2—21no—
178C2—41no—
179C2—9761no—
180C2#2146080211yescharacteristic
subgroupG/H
centerC2#21460802
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
FittingC61×#338C4
socleC2×C61#1345
prime radical#16840562C4
cosocle#16839785C22
hypercenter#338#6923
hypocenterC61#7415
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #338

Complements

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

NH ≅ G/Ntype
1. #21460766C2semidirect
2. #21460725C2semidirect
101. C61#7415semidirect

Maximal subgroups

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

subgroupindex
#214607662
#214607252
#214471072
#741561