Finite Group Databasebeta

← #29600833

Subgroups — #29600833

Order 15616.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#21448134C211yesmaximal, characteristic, complemented
2#21448132C211yesmaximal, characteristic, complemented
3#21448067C211yesmaximal, characteristic, complemented
4#21447699C211yesmaximal, characteristic, complemented
5#21444016C211yesmaximal, characteristic, complemented
6#21444008C211yesmaximal, characteristic, complemented
7C61×#1419C211yesmaximal, characteristic, complemented
8#16840194C2211yescharacteristic
9C2×D976C2211yescharacteristic
10C2×#14519718—21no—
11#16840137—21no—
12#16839878—21no—
13#16839601—21no—
14#16839600—21no—
15D1952—21no—
16#16839597—21no—
17#16839596C2211yescharacteristic
18#16839568—21no—
19C16×Dic61C2211yescharacteristic
20C2×D16×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519799—21no—
24C2×D488—21no—
25C2×#11758199—41no—
26#14519785—41no—
27#14519773—41no—
28Dic488D411yescharacteristic, complemented
29#14519722—21no—
30D976—21no—
31D976—21no—
32D976D411yescharacteristic, complemented
33#14519718—42no—
34C2×#11758185D411yescharacteristic
35#14519703—41no—
36C8×Dic61D411yescharacteristic
37#14519683—21no—
38C2×D8×C61—21no—
39D16×C61—21no—
40D16×C61—21no—
41C2×C16×C61C2311yescharacteristic
42#108×C61—21no—
43C32×C61—21no—
44C2×D4×C61—41no—
45C2×C22⋊D61—82no—
46#11758222—41no—
47C2×D244—41no—
48D8×C61—41no—
49D8×C61—41no—
50M16×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52#11758199—81no—
53#11758199—81no—
54C4×Dic61D811yescharacteristic
55C2×#92418D811yescharacteristic
56Dic244—21no—
57D488—21no—
58D488—41no—
59D488—41no—
60#11758190—41no—
61#11758189—81no—
62C8×D61—81no—
63C16×C61C2×D411yescharacteristic
64C16×C61#4111yescharacteristic
65#11758185—21no—
66C23×C61—81no—
67C22×D61—81no—
68D4×C61—81no—
69D4×C61—81no—
70C2×C4×C61C2×D811yescharacteristic
71C22⋊D61—81no—
72C22⋊D61—164no—
73C2×Dic61—21no—
74D244—41no—
75D244—81no—
76D244—81no—
77C4×D61—81no—
78Dic122—41no—
79C8×C61—81no—
80C8×C61#12111yescharacteristic
81C8×C61AGL(1,ℤ/8)11yescharacteristic
82#92418D1611yescharacteristic
83#92418D1611yescharacteristic
84#13692—611nomaximal, Sylow
85C22×C61—162no—
86C22×C61—161no—
87C22×C61#50911yescharacteristic
88C2×D61—81no—
89C2×D61—162no—
90C2×D61—161no—
91C4×C61#45911yescharacteristic
92C4×C61C2×D1611yescharacteristic
93Dic61—22no—
94Dic61—81no—
95#2263—611no—
96#2263—611no—
97#2246—611no—
98#2178—611no—
99#1422—611no—
100#1419—611no—
101#1419D6111yescharacteristic, complemented
102C2×C61—21no—
103C2×C61—321no—
104C2×C61#220611yescharacteristic
105D61—161no—
106D61—321no—
107#508—611no—
108C2×D16—611no—
109C2×D16—1221no—
110C2×D16C2×D6111yescharacteristic
111#493—1221no—
112#443—1221no—
113SD64—1221no—
114SD64—1221no—
115D32—1221no—
116D32—1221no—
117M64—611no—
118M64C2×D6111yescharacteristic
119#368C2×D6111yescharacteristic
120#359—1221no—
121C4×C16—611no—
122C61#1369211yescharacteristic, complemented, Sylow
123#135—1221no—
124C2×D8—21no—
125C2×D8—1221no—
126C2×D8—2441no—
127#131—2441no—
128#127—2441no—
129Q32—611no—
130SD32—1221no—
131D16—21no—
132D16—21no—
133D16—611no—
134D16—1221no—
135D16—1221no—
136D16—2442no—
137C2×C16—611no—
138C2×C16C22×D6111yescharacteristic
139#108—21no—
140#104—2441no—
141C4×C8—611no—
142C32—21no—
143C32—1221no—
144#41—2441no—
145C2×D4—41no—
146C2×D4—4882no—
147C2×D4—2441no—
148Q16—1221no—
149SD16—2441no—
150D8—41no—
151D8—41no—
152D8—1221no—
153D8—4881no—
154D8—4881no—
155D8—2441no—
156D8—2441no—
157M16—41no—
158M16—4881no—
159C2×C8—611no—
160C2×C8—4881no—
161C2×C8D4×D6111yescharacteristic
162C42—611no—
163C16—1221no—
164C16#1175822211yescharacteristic
165C16D4×D6111yescharacteristic
166C23—81no—
167C23—4881no—
168Q8—2441no—
169D4—81no—
170D4—81no—
171D4—9764no—
172D4—4881no—
173D4—4881no—
174D4—4881no—
175D4—2441no—
176C2×C4—1221no—
177C2×C4—4881no—
178C2×C4D8×D6111yescharacteristic
179C8—81no—
180C8—611no—
181C8—611no—
182C8#1451975011yescharacteristic
183C8#1451980411yescharacteristic
184C22—162no—
185C22—161no—
186C22—9762no—
187C22—9761no—
188C22—4881no—
189C22#1684019911yescharacteristic
190C4—1222no—
191C4—4881no—
192C4#1683995611yescharacteristic
193C4D16×D6111yescharacteristic
194C2—21no—
195C2—321no—
196C2—19521no—
197C2—9761no—
198C2#2144785311yescharacteristic
subgroupG/H
centerC2#21447853
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1419C2
socleC2×C61#2206
hypercenter#1419D61
hypocenterC61#13692
LCSG ▷ C2×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
1. #21448134C2semidirect
2. #21448132C2semidirect
3. #21448067C2semidirect
4. #21447699C2semidirect
5. #21444016C2semidirect
6. #21444008C2semidirect
7. C61×#1419C2semidirect
28. Dic488D4semidirect
32. D976D4semidirect
101. #1419D61semidirect
122. C61#13692semidirect

Maximal subgroups

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

subgroupindex
#214481342
#214481322
#214480672
#214476992
#214440162
#214440082
C61×#14192
#1369261