Finite Group Databasebeta

← #29600838

Subgroups — #29600838

Order 15616.

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

normal subgroups only

This group has 196 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#21448139C211yesmaximal, characteristic
2#21448137C211yesmaximal, characteristic
3#21448070C211yesmaximal, characteristic, complemented
4#21447699C211yesmaximal, characteristic
5#21444016C211yesmaximal, characteristic, complemented
6#21444011C211yesmaximal, characteristic, complemented
7C61×#1420C211yesmaximal, characteristic, complemented
8#16840194C2211yescharacteristic
9C2×Dic488C2211yescharacteristic
10C2×#14519723—21no—
11#16840140—21no—
12#16839878—21no—
13Dic976—21no—
14#16839602—21no—
15#16839601—21no—
16#16839599—21no—
17#16839596C2211yescharacteristic
18#16839568—21no—
19C16×Dic61C2211yescharacteristic
20C2×Q32×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519799—21no—
24C2×Dic244—21no—
25C2×#11758202—41no—
26#14519785—41no—
27#14519775—41no—
28Dic488—21no—
29Dic488—21no—
30Dic488D411yescharacteristic
31#14519723—42no—
32#14519722—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×Dic122—41no—
47Q16×C61—41no—
48Q16×C61—41no—
49M16×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51#11758202—81no—
52#11758202—81no—
53#11758196—82no—
54C4×Dic61D811yescharacteristic
55C2×#92418D811yescharacteristic
56Dic244—21no—
57Dic244—41no—
58Dic244—41no—
59D488—21no—
60#11758190—41no—
61#11758189—81no—
62C8×D61—81no—
63C16×C61C2×D411yescharacteristic
64C16×C61#4111yescharacteristic
65#11758185—21no—
66Q8×C61—81no—
67Q8×C61—81no—
68C2×C4×C61—81no—
69C2×C4×C61C2×D811yescharacteristic
70C22⋊D61—81no—
71C2×Dic61—21no—
72C2×Dic61—81no—
73D244—41no—
74C4×D61—81no—
75Dic122—41no—
76Dic122—81no—
77Dic122—81no—
78C8×C61—81no—
79C8×C61#12111yescharacteristic
80C8×C61AGL(1,ℤ/8)11yescharacteristic
81#92418D1611yescharacteristic
82#92418D1611yescharacteristic
83#13693—611nomaximal, Sylow
84C22×C61#50911yescharacteristic
85C2×D61—81no—
86C4×C61—161no—
87C4×C61#45911yescharacteristic
88C4×C61C2×D1611yescharacteristic
89Dic61—22no—
90Dic61—81no—
91Dic61—161no—
92#2264—611no—
93#2264—611no—
94#2247—611no—
95#2178—611no—
96#1422—611no—
97#1420—611no—
98#1420D6111yescharacteristic, complemented
99C2×C61—21no—
100C2×C61#220611yescharacteristic
101D61—161no—
102#508—611no—
103C2×Q32—611no—
104C2×Q32—1221no—
105C2×Q32C2×D6111yescharacteristic
106#494—1221no—
107#443—1221no—
108Q64—1221no—
109Q64—1221no—
110SD64—1221no—
111SD64—1221no—
112M64—611no—
113M64C2×D6111yescharacteristic
114#368C2×D6111yescharacteristic
115#359—1221no—
116C4×C16—611no—
117C61#1369311yescharacteristic, complemented, Sylow
118#135—1221no—
119C2×Q16—21no—
120C2×Q16—1221no—
121C2×Q16—2441no—
122#131—2441no—
123C4⋊Q8—2441no—
124Q32—21no—
125Q32—21no—
126Q32—611no—
127Q32—1221no—
128Q32—1221no—
129Q32—2442no—
130SD32—1221no—
131D16—611no—
132C2×C16—611no—
133C2×C16C22×D6111yescharacteristic
134#108—21no—
135#104—2441no—
136C4×C8—611no—
137C32—21no—
138C32—1221no—
139#41—2441no—
140C2×Q8—41no—
141C2×Q8—2441no—
142Q16—41no—
143Q16—41no—
144Q16—1221no—
145Q16—4881no—
146Q16—4881no—
147Q16—2441no—
148Q16—2441no—
149SD16—2441no—
150D8—1221no—
151M16—41no—
152M16—4881no—
153C2×C8—611no—
154C2×C8—4881no—
155C2×C8D4×D6111yescharacteristic
156C4⋊C4—4882no—
157C42—611no—
158C16—1221no—
159C16#1175822211yescharacteristic
160C16D4×D6111yescharacteristic
161Q8—81no—
162Q8—81no—
163Q8—4881no—
164Q8—4881no—
165Q8—2441no—
166D4—4881no—
167D4—2441no—
168C2×C4—81no—
169C2×C4—1221no—
170C2×C4—4881no—
171C2×C4—4881no—
172C2×C4D8×D6111yescharacteristic
173C8—81no—
174C8—611no—
175C8—611no—
176C8#1451975011yescharacteristic
177C8#1451980411yescharacteristic
178C22—4881no—
179C22#1684019911yescharacteristic
180C4—161no—
181C4—1222no—
182C4—9761no—
183C4—4881no—
184C4#1683995611yescharacteristic
185C4D16×D6111yescharacteristic
186C2—21no—
187C2—9761no—
188C2#2144785311yescharacteristic
subgroupG/H
centerC2#21447853
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1420C2
socleC2×C61#2206
prime radical#16840194C22
hypercenter#1420D61
hypocenterC61#13693
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
3. #21448070C2semidirect
5. #21444016C2semidirect
6. #21444011C2semidirect
7. C61×#1420C2semidirect
98. #1420D61semidirect
117. C61#13693semidirect

Maximal subgroups

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

subgroupindex
#214481392
#214481372
#214480702
#214476992
#214440162
#214440112
C61×#14202
#1369361