Finite Group Databasebeta

← #29600830

Subgroups — #29600830

Order 15616.

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

normal subgroups only

This group has 200 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#21448137C211yesmaximal, characteristic, complemented
2#21448134C211yesmaximal, characteristic
3#21448081C211yesmaximal, characteristic, complemented
4#21447699C211yesmaximal, characteristic, complemented
5#21444016C211yesmaximal, characteristic, complemented
6#21444008C211yesmaximal, characteristic, complemented
7C61×#1420C211yesmaximal, characteristic, complemented
8#16840194C2211yescharacteristic
9C2×#14519720—21no—
10C2×D976C2211yescharacteristic
11#16840147—21no—
12#16839878—21no—
13#16839602—21no—
14#16839601—21no—
15#16839599—21no—
16D1952—21no—
17#16839596C2211yescharacteristic
18#16839568—21no—
19C16×Dic61C2211yescharacteristic
20C2×Q32×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519799—21no—
24C2×#11758201—41no—
25C2×D488—21no—
26#14519785—41no—
27#14519766—41no—
28Dic488D411yescharacteristic
29#14519722—21no—
30#14519720—42no—
31D976—21no—
32D976—21no—
33D976D411yescharacteristic
34C2×#11758185D411yescharacteristic
35#14519703—41no—
36C8×Dic61D411yescharacteristic
37#14519683—21no—
38C2×Q16×C61—21no—
39Q32×C61—21no—
40Q32×C61—21no—
41C2×C16×C61C2311yescharacteristic
42#108×C61—21no—
43C32×C61—21no—
44C2×Q8×C61—41no—
45#11758222—41no—
46C2×D244—41no—
47Q16×C61—41no—
48Q16×C61—41no—
49M16×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51#11758201—81no—
52#11758201—81no—
53#11758198—82no—
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—
66C22×D61—81no—
67Q8×C61—81no—
68Q8×C61—81no—
69C2×C4×C61—81no—
70C2×C4×C61C2×D811yescharacteristic
71C22⋊D61—81no—
72C2×Dic61—21no—
73D244—41no—
74D244—81no—
75D244—81no—
76C4×D61—81no—
77Dic122—41no—
78C8×C61—81no—
79C8×C61#12111yescharacteristic
80C8×C61AGL(1,ℤ/8)11yescharacteristic
81#92418D1611yescharacteristic
82#92418D1611yescharacteristic
83#13691—611nomaximal, Sylow
84C22×C61#50911yescharacteristic
85C2×D61—81no—
86C2×D61—162no—
87C2×D61—161no—
88C4×C61—161no—
89C4×C61#45911yescharacteristic
90C4×C61C2×D1611yescharacteristic
91Dic61—41no—
92Dic61—81no—
93#2264—611no—
94#2263—611no—
95#2249—611no—
96#2178—611no—
97#1422—611no—
98#1420D6111yescharacteristic, complemented
99#1419—611no—
100C2×C61—21no—
101C2×C61#220611yescharacteristic
102D61—161no—
103D61—321no—
104#508—611no—
105C2×Q32C2×D6111yescharacteristic
106C2×SD32—1221no—
107C2×D16—611no—
108#495—1221no—
109#443—1221no—
110Q64—1221no—
111SD64—1221no—
112SD64—1221no—
113D32—1221no—
114M64—611no—
115M64C2×D6111yescharacteristic
116#368C2×D6111yescharacteristic
117#359—1221no—
118C4×C16—611no—
119C61#1369111yescharacteristic, complemented, Sylow
120#135—1221no—
121C2×Q16—21no—
122C2×SD16—2441no—
123C2×D8—1221no—
124#131—2441no—
125#124—2441no—
126Q32—21no—
127Q32—21no—
128Q32—611no—
129SD32—1221no—
130SD32—2442no—
131D16—611no—
132D16—1221no—
133D16—1221no—
134C2×C16—611no—
135C2×C16C22×D6111yescharacteristic
136#108—21no—
137#104—2441no—
138C4×C8—611no—
139C32—21no—
140C32—1221no—
141#41—2441no—
142C2×Q8—41no—
143C2×D4—2441no—
144Q16—41no—
145Q16—41no—
146Q16—1221no—
147SD16—4881no—
148SD16—4881no—
149SD16—2441no—
150D8—1221no—
151D8—2441no—
152D8—2441no—
153M16—41no—
154M16—4881no—
155C2×C8—611no—
156C2×C8—4881no—
157C2×C8D4×D6111yescharacteristic
158C22⋊C4—4882no—
159C42—611no—
160C16—1221no—
161C16#1175822211yescharacteristic
162C16D4×D6111yescharacteristic
163C23—4881no—
164Q8—81no—
165Q8—81no—
166Q8—2441no—
167D4—4881no—
168D4—4881no—
169D4—4881no—
170D4—2441no—
171C2×C4—81no—
172C2×C4—1221no—
173C2×C4—4881no—
174C2×C4D8×D6111yescharacteristic
175C8—81no—
176C8—611no—
177C8—611no—
178C8#1451975011yescharacteristic
179C8#1451980411yescharacteristic
180C22—9762no—
181C22—9761no—
182C22—4881no—
183C22#1684019911yescharacteristic
184C4—161no—
185C4—4881no—
186C4—2441no—
187C4#1683995611yescharacteristic
188C4D16×D6111yescharacteristic
189C2—21no—
190C2—19521no—
191C2—9761no—
192C2#2144785311yescharacteristic
subgroupG/H
centerC2#21447853
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1420C2
socleC2×C61#2206
prime radical#21448134C2
hypercenter#1420D61
hypocenterC61#13691
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. #21448137C2semidirect
3. #21448081C2semidirect
4. #21447699C2semidirect
5. #21444016C2semidirect
6. #21444008C2semidirect
7. C61×#1420C2semidirect
98. #1420D61semidirect
119. C61#13691semidirect

Maximal subgroups

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

subgroupindex
#214481372
#214481342
#214480812
#214476992
#214440162
#214440082
C61×#14202
#1369161