Finite Group Databasebeta

← #29600641

Subgroups — #29600641

Order 15616.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448132C211yesmaximal, characteristic
2#21447704C211yesmaximal, characteristic, complemented
3#21447695C211yesmaximal, characteristic, complemented
4#21444026C211yesmaximal, characteristic, complemented
5#21444007C211yesmaximal, characteristic, complemented
6#21443954C211yesmaximal, characteristic, complemented
7C61×#1419C211yesmaximal, characteristic, complemented
8#16840194C2211yescharacteristic
9#16839878—21no—
10D8×Dic61—21no—
11#16839600C412yescomplemented
12#16839597C412yescomplemented
13#16839596C2211yescharacteristic
14#16839590C2211yescharacteristic
15#16839568—21no—
16#16839563—21no—
17#16839537C2211yescharacteristic
18C2×D16×C61C2211yescharacteristic
19C61×M64C2211yescharacteristic
20C61×#368C2211yescharacteristic
21#14519799—21no—
22#14519785—41no—
23D4×Dic61—41no—
24Dic488C2×C411yescharacteristic, complemented
25#14519722—21no—
26D976C2×C411yescharacteristic, complemented
27C2×#11758185D411yescharacteristic
28#14519711—21no—
29#14519703—41no—
30#14519698—41no—
31C8×Dic61D411yescharacteristic
32#14519683C2×C412yescomplemented
33C2×D8×C61—21no—
34D16×C61—21no—
35D16×C61C2×C412yes—
36C2×C16×C61C2311yescharacteristic
37#108×C61—21no—
38C32×C61—21no—
39C2×D4×C61—41no—
40C22×Dic61—81no—
41#11758222—41no—
42D8×C61—22no—
43D8×C61—41no—
44M16×C61—41no—
45C2×C8×C61C2×D411yescharacteristic
46C22⋊Dic61—81no—
47C4⋊Dic61—41no—
48C4×Dic61D811yescharacteristic
49C2×#92418D811yescharacteristic
50Dic244—21no—
51D488—21no—
52#11758190—41no—
53#11758189—81no—
54C8×D61—81no—
55C16×C61C22×C411yescharacteristic
56C16×C61#4111yescharacteristic
57#11758185—21no—
58C23×C61—81no—
59D4×C61—42no—
60D4×C61—81no—
61C2×C4×C61C2×D811yescharacteristic
62C22⋊D61—81no—
63C2×Dic61—21no—
64C2×Dic61—81no—
65C2×Dic61—162no—
66D244—41no—
67C4×D61—81no—
68Dic122—41no—
69C8×C61—81no—
70C8×C61C4×D411yescharacteristic
71C8×C61#13511yescharacteristic
72#92418—21no—
73#13658—611nomaximal, Sylow
74C22×C61—82no—
75C22×C61—161no—
76C22×C61—161no—
77C22×C61#50911yescharacteristic
78C2×D61—81no—
79C4×C61C4×D811yescharacteristic
80C4×C61#50911yescharacteristic
81Dic61—41no—
82Dic61—81no—
83Dic61—161no—
84#2263—611no—
85#2179—611no—
86#2177—611no—
87#1426—611no—
88#1419D6111yescharacteristic, complemented
89#1418—611no—
90#1398—611no—
91C2×C61—21no—
92C2×C61—162no—
93C2×C61#217711yescharacteristic
94D61—161no—
95#508—611no—
96C2×D16C2×D6111yescharacteristic
97#443—1221no—
98C4×D8—1221no—
99SD64—612no—
100D32—612no—
101M64—611no—
102M64C2×D6111yescharacteristic
103#368C2×D6111yescharacteristic
104#367—611no—
105#359—1221no—
106#357—1221no—
107#346—611no—
108C61#1365811yescharacteristic, complemented, Sylow
109#135—1221no—
110C2×D8—21no—
111#131—2441no—
112C4×D4—2441no—
113Q32—611no—
114SD32—1221no—
115D16—21no—
116D16—611no—
117D16C4×D6112yes—
118C2×C16—611no—
119C2×C16C22×D6111yescharacteristic
120#108—21no—
121#107—1221no—
122#104—2441no—
123#102—2441no—
124C4×C8—611no—
125C32—21no—
126C32—612no—
127#41—2441no—
128C2×D4—41no—
129C22×C4—4881no—
130Q16—1221no—
131SD16—2441no—
132D8—22no—
133D8—41no—
134D8—1221no—
135M16—41no—
136M16—4881no—
137C2×C8—611no—
138C2×C8—4881no—
139C2×C8D4×D6111yescharacteristic
140C4⋊C4—2441no—
141C22⋊C4—4881no—
142C42—611no—
143C16—1221no—
144C16C2×C4×D6111yescharacteristic
145C16#1175822411yescharacteristic
146C23—81no—
147Q8—2441no—
148D4—42no—
149D4—81no—
150D4—4881no—
151D4—2441no—
152C2×C4—1221no—
153C2×C4—9762no—
154C2×C4—4881no—
155C2×C4—4881no—
156C2×C4D8×D6111yescharacteristic
157C8—81no—
158C8—1221no—
159C8#1451973711yescharacteristic
160C8#1451979811yescharacteristic
161C22—82no—
162C22—161no—
163C22—161no—
164C22—4881no—
165C22#1684019911yescharacteristic
166C4—9761no—
167C4—4881no—
168C4—2441no—
169C4#1683984211yescharacteristic
170C4#1684019611yescharacteristic
171C2—21no—
172C2—162no—
173C2—9761no—
174C2#2144769211yescharacteristic
subgroupG/H
centerC2#21447692
commutatorC16×C61C22×C4
FrattiniC2×C16C22×D61
FittingC61×#1419C2
socleC2×C61#2177
prime radical#21448132C2
cosocleC2×C16×C61C23
hypercenter#1419D61
hypocenterC61#13658
LCSG ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
2. #21447704C2semidirect
3. #21447695C2semidirect
4. #21444026C2semidirect
5. #21444007C2semidirect
6. #21443954C2semidirect
7. C61×#1419C2semidirect
11. #16839600C4semidirect
12. #16839597C4semidirect
24. Dic488C2×C4semidirect
26. D976C2×C4semidirect
32. #14519683C2×C4semidirect
88. #1419D61semidirect
108. C61#13658semidirect

Maximal subgroups

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

subgroupindex
#214481322
#214477042
#214476952
#214440262
#214440072
#214439542
C61×#14192
#1365861