Finite Group Databasebeta

← #29600828

Subgroups — #29600828

Order 15616.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#21448139C211yesmaximal, characteristic, complemented
2#21448134C211yesmaximal, characteristic
3#21448080C211yesmaximal, characteristic, complemented
4#21447701C211yesmaximal, characteristic, complemented
5#21444013C211yesmaximal, characteristic, complemented
6#21444010C211yesmaximal, characteristic, complemented
7C61×#1422C211yesmaximal, characteristic, complemented
8#16840194C2211yescharacteristic
9C2×Dic488C2211yescharacteristic
10C2×#14519722—21no—
11C2×D976C2211yescharacteristic
12#16840146—21no—
13#16839880—21no—
14Dic976—21no—
15#16839601—21no—
16#16839601—21no—
17D1952—21no—
18#16839592C2211yescharacteristic
19#16839570—21no—
20C61×M64C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C4×C16×C61C2211yescharacteristic
23#14519799—21no—
24C2×Dic244—21no—
25C2×#11758190—41no—
26C2×D488—21no—
27#14519783—41no—
28#14519765—41no—
29Dic488—21no—
30Dic488—21no—
31Dic488D411yescharacteristic
32#14519722—21no—
33#14519722—42no—
34D976—21no—
35D976—21no—
36D976D411yescharacteristic
37#14519713—21no—
38#14519705—41no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61C2311yescharacteristic
41C4×C8×C61D411yescharacteristic
42C32×C61—21no—
43C32×C61—21no—
44#11758222—41no—
45C2×D244—41no—
46C2×Dic122—41no—
47C2×C8×C61D811yescharacteristic
48C2×C8×C61C2×D411yescharacteristic
49C42×C61D811yescharacteristic
50#11758198—82no—
51#11758194—41no—
52Dic244—21no—
53Dic244—41no—
54Dic244—41no—
55D488—21no—
56D488—41no—
57D488—41no—
58#11758190—41no—
59#11758190—81no—
60#11758190—81no—
61#11758189—81no—
62C8×D61—81no—
63C16×C61—21no—
64C16×C61C2×D411yescharacteristic
65C16×C61#4111yescharacteristic
66C22×D61—81no—
67C2×C4×C61—21no—
68C2×C4×C61C2×D811yescharacteristic
69C22⋊D61—81no—
70C2×Dic61—81no—
71D244—41no—
72D244—81no—
73D244—81no—
74C4×D61—81no—
75Dic122—41no—
76Dic122—81no—
77Dic122—81no—
78C8×C61D1611yescharacteristic
79C8×C61D1611yescharacteristic
80C8×C61#12111yescharacteristic
81C8×C61AGL(1,ℤ/8)11yescharacteristic
82#92418—81no—
83#13691—611nomaximal, Sylow
84C22×C61#50911yescharacteristic
85C2×D61—81no—
86C2×D61—162no—
87C2×D61—161no—
88C4×C61—41no—
89C4×C61#45911yescharacteristic
90C4×C61C2×D1611yescharacteristic
91Dic61—81no—
92Dic61—161no—
93#2264—611no—
94#2263—611no—
95#2249—611no—
96#2178—611no—
97#1422D6111yescharacteristic, complemented
98#1420—611no—
99#1419—611no—
100C2×C61—21no—
101C2×C61#220611yescharacteristic
102D61—161no—
103D61—321no—
104#508—611no—
105C2×Q32—611no—
106C2×SD32—1221no—
107C2×D16—611no—
108#495—1221no—
109#443—1221no—
110Q64—1221no—
111SD64—1221no—
112SD64—1221no—
113D32—1221no—
114M64C2×D6111yescharacteristic
115M64C2×D6111yescharacteristic
116#368—611no—
117#359—1221no—
118C4×C16C2×D6111yescharacteristic
119C61#1369111yescharacteristic, complemented, Sylow
120#135—1221no—
121C2×Q16—1221no—
122C2×SD16—2441no—
123C2×D8—1221no—
124#131—2441no—
125#124—2441no—
126Q32—611no—
127Q32—1221no—
128Q32—1221no—
129SD32—1221no—
130SD32—2442no—
131D16—611no—
132D16—1221no—
133D16—1221no—
134C2×C16D24411yescharacteristic
135C2×C16C22×D6111yescharacteristic
136#108—1221no—
137#104—2441no—
138C4×C8D24411yescharacteristic
139C32—21no—
140C32—21no—
141#41—2441no—
142C2×Q8—2441no—
143C2×D4—2441no—
144Q16—1221no—
145Q16—2441no—
146Q16—2441no—
147SD16—4881no—
148SD16—4881no—
149SD16—2441no—
150D8—1221no—
151D8—2441no—
152D8—2441no—
153M16—4881no—
154M16—2441no—
155C2×C8—4881no—
156C2×C8D48811yescharacteristic
157C2×C8C2×D24411yescharacteristic
158C22⋊C4—4882no—
159C42D48811yescharacteristic
160C16—21no—
161C16D4×D6111yescharacteristic
162C16#1175822611yescharacteristic
163C23—4881no—
164Q8—4881no—
165Q8—4881no—
166Q8—2441no—
167D4—4881no—
168D4—4881no—
169D4—4881no—
170D4—2441no—
171C2×C4—21no—
172C2×C4—4881no—
173C2×C4—4881no—
174C2×C4C2×D48811yescharacteristic
175C8—4881no—
176C8D97611yescharacteristic
177C8D97611yescharacteristic
178C8#1451975211yescharacteristic
179C8#1451980511yescharacteristic
180C22—9762no—
181C22—9761no—
182C22—4881no—
183C22#1684020011yescharacteristic
184C4—41no—
185C4—9761no—
186C4—4881no—
187C4#1683995811yescharacteristic
188C4C2×D97611yescharacteristic
189C2—21no—
190C2—19521no—
191C2—9761no—
192C2#2144785511yescharacteristic
subgroupG/H
centerC2#21447855
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1422C2
socleC2×C61#2206
prime radical#21448134C2
hypercenter#1422D61
hypocenterC61#13691
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ C4×C16 ◁ #1422

Complements

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

NH ≅ G/Ntype
1. #21448139C2semidirect
3. #21448080C2semidirect
4. #21447701C2semidirect
5. #21444013C2semidirect
6. #21444010C2semidirect
7. C61×#1422C2semidirect
97. #1422D61semidirect
119. C61#13691semidirect

Maximal subgroups

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

subgroupindex
#214481392
#214481342
#214480802
#214477012
#214440132
#214440102
C61×#14222
#1369161