Finite Group Databasebeta

← #29600887

Subgroups — #29600887

Order 15616.

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

normal subgroups only

This group has 184 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
1C2×#16839600C211yesmaximal, characteristic, complemented
2#21448114C211yesmaximal, characteristic, complemented
3#21447945C211yesmaximal, characteristic, complemented
4#21447936C211yesmaximal, characteristic
5#21444022C211yesmaximal, characteristic, complemented
6#21444013C211yesmaximal, characteristic, complemented
7C61×#1419C211yesmaximal, characteristic, complemented
8C2×Dic488C2211yescharacteristic
9#16840178C2211yescharacteristic
10#16840038—21no—
11#16840029—21no—
12#16839600—21no—
13#16839600—21no—
14#16839595—21no—
15C2×#14519683C2211yescharacteristic
16C32×D61—21no—
17#16839592C2211yescharacteristic
18#16839577—21no—
19#16839575—21no—
20C2×D16×C61C2211yescharacteristic
21C61×M64C2211yescharacteristic
22C61×#368C2211yescharacteristic
23#14519810—41no—
24#14519803—41no—
25C2×Dic244—21no—
26#14519783D411yescharacteristic
27Dic488—21no—
28Dic488—21no—
29#14519717D411yescharacteristic
30#14519716—21no—
31C16×D61—21no—
32#14519713—21no—
33#14519695—41no—
34#14519694—41no—
35#14519683D411yescharacteristic
36#14519683D411yescharacteristic
37C2×D8×C61—21no—
38D16×C61—21no—
39D16×C61—21no—
40C2×C16×C61C2311yescharacteristic
41#108×C61—21no—
42C32×C61—21no—
43C2×D4×C61—41no—
44#11758222D811yescharacteristic
45C2×Dic122—41no—
46D8×C61—41no—
47D8×C61—41no—
48M16×C61—41no—
49C2×C8×C61C2×D411yescharacteristic
50#11758200—81no—
51#11758199—81no—
52#11758194—41no—
53#11758194D811yescharacteristic
54Dic244—41no—
55Dic244—41no—
56Dic244—81no—
57#11758190—81no—
58#11758189—21no—
59C8×D61—21no—
60C16×C61C2×D411yescharacteristic
61C16×C61#4111yescharacteristic
62#11758185—21no—
63C23×C61—81no—
64D4×C61—81no—
65D4×C61—81no—
66C2×C4×C61C2×D811yescharacteristic
67C22⋊D61—21no—
68C2×Dic61—81no—
69D244D1611yescharacteristic
70C4×D61—21no—
71Dic122—81no—
72Dic122—81no—
73Dic122D1611yescharacteristic
74C8×C61—81no—
75C8×C61#12111yescharacteristic
76C8×C61#13511yescharacteristic
77#92418—21no—
78#92418—81no—
79#13702—611nomaximal, Sylow
80C22×C61—161no—
81C22×C61—321no—
82C22×C61#50811yescharacteristic
83C2×D61—21no—
84C4×C61#46611yescharacteristic
85C4×C61C2×D1611yescharacteristic
86Dic61—21no—
87Dic61—161no—
88C2×SD64—611no—
89#2258—611no—
90#2222—611no—
91#2221—611no—
92#1425—611no—
93#1420—611no—
94#1419D6111yescharacteristic, complemented
95C2×C61—21no—
96C2×C61—321no—
97C2×C61#221511yescharacteristic
98D61—41no—
99C2×Q32—611no—
100C2×D16C2×D6111yescharacteristic
101#504—611no—
102#473—1221no—
103#472—1221no—
104SD64—1221no—
105SD64—1221no—
106M64—1221no—
107M64C2×D6111yescharacteristic
108C2×C32—611no—
109C2×C32—1221no—
110#368—611no—
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—21no—
119#131—611no—
120Q32—1221no—
121Q32—1221no—
122D16—21no—
123D16—21no—
124M32—611no—
125M32—1221no—
126C2×C16—1221no—
127C2×C16C22×D6111yescharacteristic
128#108—21no—
129#108—1221no—
130#101—2441no—
131#100—2441no—
132C32—21no—
133C32—611no—
134C32—611no—
135#41—611no—
136C2×Q8—2441no—
137C2×D4—41no—
138Q16—4881no—
139Q16—2441no—
140Q16—2441no—
141SD16—4881no—
142SD16—4881no—
143D8—41no—
144D8—41no—
145D8—4881no—
146M16—41no—
147M16—611no—
148M16—1221no—
149M16—2441no—
150C2×C8—1221no—
151C2×C8D4×D6111yescharacteristic
152C16—1221no—
153C16#1175822211yescharacteristic
154C16D4×D6111yescharacteristic
155C23—81no—
156Q8—611no—
157Q8—4881no—
158Q8—4881no—
159D4—81no—
160D4—81no—
161D4—611no—
162D4—1221no—
163C2×C4—1221no—
164C2×C4—4881no—
165C2×C4D8×D6111yescharacteristic
166C8—81no—
167C8—1221no—
168C8—4881no—
169C8#1451975011yescharacteristic
170C8#1451979811yescharacteristic
171C22—161no—
172C22—321no—
173C22—1221no—
174C22#1684019311yescharacteristic
175C4—1221no—
176C4—9761no—
177C4#1683999711yescharacteristic
178C4D16×D6111yescharacteristic
179C2—21no—
180C2—321no—
181C2—2441no—
182C2#2144790411yescharacteristic
subgroupG/H
centerC2#21447904
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1419C2
socleC2×C61#2215
prime radical#21447936C2
hypercenter#1419D61
hypocenterC61#13702
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. C2×#16839600C2semidirect
2. #21448114C2semidirect
3. #21447945C2semidirect
5. #21444022C2semidirect
6. #21444013C2semidirect
7. C61×#1419C2semidirect
94. #1419D61semidirect
114. C61#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#168396002
#214481142
#214479452
#214479362
#214440222
#214440132
C61×#14192
#1370261