Finite Group Databasebeta

← #30594978

Subgroups — #30594978

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#21447103C211yesmaximal, characteristic
4#16840783—21no—
5#16840658—21no—
6#16839785C2211yescharacteristic
7C2×#14519704—21no—
8#16839746—21no—
9#16839520C411yescharacteristic
10C61×#575C411yescharacteristic
11#14519851—41no—
12C4⋊#92420—41no—
13C22⋊#92420—22no—
14#14519832—41no—
15C2×#11758194—21no—
16C2×#11758194D411yescharacteristic
17C2×C4×Dic61D411yescharacteristic
18#14519706—41no—
19#14519704—41no—
20#14519704—41no—
21#14519696—41no—
22#14519694—41no—
23C2×#41×C61—21no—
24#137×C61—41no—
25AGL(1,ℤ/8)×C61—41no—
26#135×C61—41no—
27C2×M16×C61C2×C411yescharacteristic
28#41×C61—41no—
29#41×C61—41no—
30#41×C61—41no—
31#41×C61—41no—
32C2×Q8×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61C22⋊C411yescharacteristic
37C22×Dic61—21no—
38C2×#92420—42no—
39Q16×C61—41no—
40SD16×C61—42no—
41D8×C61—41no—
42M16×C61—41no—
43C2×C8×C61—21no—
44C4×Dic61—21no—
45C4×Dic61D811yescharacteristic
46C4×Dic61SD1611yescharacteristic
47#11758194—41no—
48#11758194—41no—
49#11758194—41no—
50C2×#92418—21no—
51C2×#92418—41no—
52#11758187—81no—
53C23×C61—41no—
54C23×C61#10411yescharacteristic
55Q8×C61—41no—
56Q8×C61—41no—
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—81no—
60D4×C61—81no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—81no—
65C2×C4×C61—81no—
66C2×C4×C61#9911yescharacteristic
67C2×C4×C61#10211yescharacteristic
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—81no—
71#92420—82no—
72C8×C61—41no—
73#92418—41no—
74#92418—81no—
75#7415—611nomaximal, Sylow
76C22×C61—21no—
77C22×C61—41no—
78C22×C61—81no—
79C22×C61—161no—
80C22×C61#32711yescharacteristic
81C4×C61—21no—
82C4×C61—81no—
83C4×C61AΣL(1,𝔽16)11yescharacteristic
84C4×C61#35511yescharacteristic
85Dic61—41no—
86Dic61—41no—
87#2050—611no—
88#1327—611no—
89#1307—611no—
90C2×C61—21no—
91C2×C61—41no—
92C2×C61—161no—
93C2×C61#134511yescharacteristic
94#575#692311yescharacteristic
95#432—1221no—
96#423—611no—
97C2×#104—1221no—
98#413—1221no—
99#349—1221no—
100#338—611no—
101C61#741511yescharacteristic, complemented, Sylow
102C2×#41—21no—
103#137—41no—
104AGL(1,ℤ/8)—41no—
105#135—41no—
106C2×M16—611no—
107C2×M16—1221no—
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—41no—
120#41—41no—
121#41—41no—
122#41—41no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—41no—
126C22×C4—41no—
127C22×C4—1221no—
128C22×C4C22⋊#692311yescharacteristic
129Q16—41no—
130SD16—42no—
131D8—41no—
132M16—41no—
133M16—2441no—
134M16—2441no—
135M16—2441no—
136C2×C8—21no—
137C2×C8—1221no—
138C2×C8—2441no—
139C2×C8—2442no—
140C42—611no—
141C42—611no—
142C42—1221no—
143C16—4881no—
144C23—41no—
145C23#1451984111yescharacteristic
146Q8—41no—
147Q8—41no—
148D4—41no—
149D4—41no—
150D4—81no—
151D4—81no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4—81no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—4881no—
160C2×C4#1451983511yescharacteristic
161C2×C4#1451983911yescharacteristic
162C8—41no—
163C8—4881no—
164C8—4882no—
165C8—2441no—
166C22—21no—
167C22—41no—
168C22—81no—
169C22—161no—
170C22#1684061311yescharacteristic
171C4—21no—
172C4—81no—
173C4—2441no—
174C4—2441no—
175C4#1684066211yescharacteristic
176C4#1684067011yescharacteristic
177C2—21no—
178C2—41no—
179C2—161no—
180C2#2146080111yescharacteristic
subgroupG/H
centerC2#21460801
commutatorC2×M16×C61C2×C4
FrattiniC2×M16C2×#6923
Fitting, prime radicalC61×#575C4
socleC2×C61#1345
cosocle#16839785C22
hypercenter#575#6923
hypocenterC61#7415
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ #575

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
#214471032
#741561