Finite Group Databasebeta

← #29600889

Subgroups — #29600889

Order 15616.

184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×#16839601C211yesmaximal, characteristic, complemented
2#21448112C211yesmaximal, characteristic, complemented
3#21447945C211yesmaximal, characteristic, complemented
4#21447940C211yesmaximal, characteristic
5#21444011C211yesmaximal, characteristic, complemented
6#21444008C211yesmaximal, characteristic, complemented
7C61×#1425C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9C2×D976C2211yescharacteristic
10#16840178C2211yescharacteristic
11#16840038—21no—
12#16840033—21no—
13#16839601—21no—
14#16839601—21no—
15#16839596C2211yescharacteristic
16#16839595—21no—
17C32×D61—21no—
18#16839577—21no—
19#16839574—21no—
20C2×C32×C61C2211yescharacteristic
21C61×#368C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519810—41no—
24#14519805—41no—
25C2×Dic244—21no—
26C2×D488—21no—
27#14519783D411yescharacteristic
28Dic488—21no—
29Dic488—21no—
30D976—21no—
31D976—21no—
32#14519717D411yescharacteristic
33#14519716—21no—
34C16×D61—21no—
35#14519695—41no—
36#14519693—41no—
37#14519683—21no—
38C2×C16×C61C2311yescharacteristic
39#108×C61—21no—
40#108×C61—21no—
41C32×C61D411yescharacteristic
42C32×C61D411yescharacteristic
43#11758222D811yescharacteristic
44C2×D244—41no—
45C2×Dic122—41no—
46M16×C61—41no—
47M16×C61—41no—
48C2×C8×C61C2×D411yescharacteristic
49#11758194D811yescharacteristic
50Dic244—41no—
51Dic244—41no—
52Dic244—81no—
53D488—41no—
54D488—41no—
55D488—81no—
56#11758190—81no—
57#11758190—81no—
58#11758189—21no—
59C8×D61—21no—
60C16×C61C2×D411yescharacteristic
61C16×C61#4111yescharacteristic
62#11758185—21no—
63C22×D61—81no—
64C2×C4×C61C2×D811yescharacteristic
65C22⋊D61—21no—
66C2×Dic61—81no—
67D244—81no—
68D244—81no—
69D244D1611yescharacteristic
70C4×D61—21no—
71Dic122—81no—
72Dic122—81no—
73Dic122D1611yescharacteristic
74C8×C61—81no—
75C8×C61—81no—
76C8×C61#12111yescharacteristic
77C8×C61#13511yescharacteristic
78#92418—21no—
79#13702—611nomaximal, Sylow
80C22×C61#50811yescharacteristic
81C2×D61—21no—
82C2×D61—161no—
83C2×D61—321no—
84C4×C61#46611yescharacteristic
85C4×C61C2×D1611yescharacteristic
86Dic61—21no—
87Dic61—161no—
88C2×SD64—611no—
89#2258—611no—
90#2222—611no—
91#2221—611no—
92#1425D6111yescharacteristic, complemented
93#1420—611no—
94#1419—611no—
95C2×C61—21no—
96C2×C61#221511yescharacteristic
97D61—41no—
98D61—321no—
99C2×Q32—611no—
100C2×D16—611no—
101#504—611no—
102#473—1221no—
103#472—1221no—
104SD64—1221no—
105SD64—1221no—
106M64—611no—
107M64—1221no—
108C2×C32—1221no—
109C2×C32C2×D6111yescharacteristic
110#368C2×D6111yescharacteristic
111#368C2×D6111yescharacteristic
112#362—1221no—
113#361—1221no—
114C61#1370211yescharacteristic, complemented, Sylow
115#137—2441no—
116AGL(1,ℤ/8)—2441no—
117C2×Q16—1221no—
118C2×D8—1221no—
119#131—611no—
120Q32—1221no—
121Q32—1221no—
122D16—1221no—
123D16—1221no—
124M32—611no—
125M32—1221no—
126C2×C16—1221no—
127C2×C16C22×D6111yescharacteristic
128#108—21no—
129#108—21no—
130#101—2441no—
131#100—2441no—
132C32—1221no—
133C32D24411yescharacteristic
134C32D24411yescharacteristic
135#41—611no—
136C2×Q8—2441no—
137C2×D4—2441no—
138Q16—4881no—
139Q16—2441no—
140Q16—2441no—
141SD16—4881no—
142SD16—4881no—
143D8—4881no—
144D8—2441no—
145D8—2441no—
146M16—41no—
147M16—41no—
148M16—611no—
149M16—1221no—
150C2×C8—1221no—
151C2×C8D4×D6111yescharacteristic
152C16—1221no—
153C16C2×D24411yescharacteristic
154C16#1175822611yescharacteristic
155C23—4881no—
156Q8—611no—
157Q8—4881no—
158Q8—4881no—
159D4—611no—
160D4—1221no—
161D4—4881no—
162D4—4881no—
163C2×C4—1221no—
164C2×C4—4881no—
165C2×C4D8×D6111yescharacteristic
166C8—81no—
167C8—81no—
168C8—1221no—
169C8#1451975211yescharacteristic
170C8#1451980011yescharacteristic
171C22—1221no—
172C22—19521no—
173C22—9761no—
174C22#1684019511yescharacteristic
175C4—1221no—
176C4—9761no—
177C4#1683999911yescharacteristic
178C4D16×D6111yescharacteristic
179C2—21no—
180C2—19521no—
181C2—2441no—
182C2#2144790611yescharacteristic
subgroupG/H
centerC2#21447906
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1425C2
socleC2×C61#2215
prime radical#21447940C2
hypercenter#1425D61
hypocenterC61#13702
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1425

Complements

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

NH ≅ G/Ntype
1. C2×#16839601C2semidirect
2. #21448112C2semidirect
3. #21447945C2semidirect
5. #21444011C2semidirect
6. #21444008C2semidirect
7. C61×#1425C2semidirect
92. #1425D61semidirect
114. C61#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#168396012
#214481122
#214479452
#214479402
#214440112
#214440082
C61×#14252
#1370261