Finite Group Databasebeta

← #29593374

Subgroups — #29593374

Order 15616.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#21457258C211yesmaximal, characteristic
2#21448034C212yesmaximal, complemented
3#21447399C211yesmaximal, characteristic, complemented
4#21443811C212yesmaximal, complemented
5C61×#1328C211yesmaximal, characteristic, complemented
6#16840367—21no—
7#16840063—22no—
8#16840015C2212yes—
9#16839998—21no—
10#16839958—22no—
11#16839811C2211yescharacteristic
12#16839585—22no—
13#16839576—22no—
14#16839532—21no—
15#16839527—21no—
16#16839520C2211yescharacteristic
17C61×#424C2211yescharacteristic
18C61×#349C2212yes—
19C2×D488—21no—
20C2×D488D412yes—
21C2×#11758194—21no—
22C2×#11758194—21no—
23#14519774—21no—
24#14519769—21no—
25#14519762—42no—
26#14519751—22no—
27#14519750—42no—
28C4×D244—22no—
29#14519713—22no—
30#14519711—21no—
31#14519709D412yes—
32#14519699—22no—
33#14519699—22no—
34C2×M16×C61C2311yescharacteristic
35C22×C8×C61D411yescharacteristic
36#117×C61D411yescharacteristic
37M32×C61—22no—
38C4⋊C8×C61—22no—
39C22×C4×C61C2×D411yescharacteristic
40C2×C22⋊D61—42no—
41C2×D244—22no—
42C2×D244—42no—
43C2×C4×D61—42no—
44M16×C61—41no—
45C2×C8×C61—21no—
46C2×C8×C61—41no—
47C2×C8×C61C2×D412yes—
48C4⋊C4×C61—21no—
49C22⋊C4×C61SD1612yes—
50C42×C61—21no—
51#11758198—42no—
52#11758198—42no—
53C4⋊Dic61—22no—
54#11758196—42no—
55#11758194—41no—
56#11758194—41no—
57#11758194—41no—
58#11758194—41no—
59C2×#92418—41no—
60C2×#92418—41no—
61D488—42no—
62D488—81no—
63C16×C61—42no—
64C23×C61C2×SD1611yescharacteristic
65C22×D61—42no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61#12011yescharacteristic
70C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
71C22⋊D61—162no—
72C2×Dic61—42no—
73D244—42no—
74D244—42no—
75D244—162no—
76C4×D61—162no—
77C8×C61—22no—
78C8×C61—41no—
79#92418—81no—
80#92418—81no—
81#12304—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—41no—
84C22×C61#45011yescharacteristic
85C2×D61—82no—
86C2×D61—82no—
87C2×D61—82no—
88C4×C61—21no—
89C4×C61—42no—
90C4×C61#45411yescharacteristic
91C4×C61#45811yescharacteristic
92Dic61—82no—
93#3259—611no—
94#2238—612no—
95#2103—611no—
96#1341—612no—
97#1328D6111yescharacteristic, complemented
98C2×C61—21no—
99C2×C61—41no—
100C2×C61#161611yescharacteristic
101D61—162no—
102#540—1221no—
103#478—1222no—
104#469—612no—
105#466—1221no—
106#459—1222no—
107#430—611no—
108#424C2×D6111yescharacteristic
109#365—1222no—
110#361—1222no—
111#349C2×D6112yes—
112#344—1221no—
113#341—1221no—
114#338—611no—
115C61#1230411yescharacteristic, complemented, Sylow
116C2×D8—612no—
117C2×D8—1221no—
118C2×M16—1221no—
119C2×M16—1221no—
120C2×M16C22×D6111yescharacteristic
121C22×C8D24411yescharacteristic
122#127—1221no—
123#125—1221no—
124#123—2442no—
125#121—1222no—
126#121—2442no—
127C4×D4—1222no—
128#117D24411yescharacteristic
129M32—22no—
130#108—1222no—
131#107—1221no—
132#106—612no—
133C4⋊C8—22no—
134#102—1222no—
135#102—1222no—
136C2×D4—1222no—
137C2×D4—2442no—
138C2×D4—2442no—
139C22×C4—2442no—
140C22×C4C2×D24411yescharacteristic
141D8—4881no—
142D8—2442no—
143M16—41no—
144M16—2441no—
145M16—2441no—
146M16—2441no—
147M16—2441no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—2441no—
151C2×C8—2441no—
152C2×C8D4×D6112yes—
153C4⋊C4—21no—
154C4⋊C4—1222no—
155C4⋊C4—2442no—
156C22⋊C4—2442no—
157C22⋊C4—2442no—
158C22⋊C4#1175819012yes—
159C42—21no—
160C16—42no—
161C23—2442no—
162C23C2×#1175819011yescharacteristic
163D4—9762no—
164D4—9762no—
165D4—2442no—
166D4—2442no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—9762no—
171C2×C4—2442no—
172C2×C4#1451974711yescharacteristic
173C2×C4#1451980511yescharacteristic
174C8—22no—
175C8—41no—
176C8—4881no—
177C8—4881no—
178C22—21no—
179C22—41no—
180C22—4882no—
181C22—4882no—
182C22—4882no—
183C22#1683991511yescharacteristic
184C4—21no—
185C4—42no—
186C4—4882no—
187C4#1683993711yescharacteristic
188C4#1683995311yescharacteristic
189C2—21no—
190C2—41no—
191C2—9762no—
192C2#2144485811yescharacteristic
subgroupG/H
centerC2#21444858
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
FittingC61×#1328C2
socleC2×C61#1616
prime radical#21457258C2
hypercenter#1328D61
hypocenterC61#12304
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #21448034C2semidirect
3. #21447399C2semidirect
4. #21443811C2semidirect
5. C61×#1328C2semidirect
97. #1328D61semidirect
115. C61#12304semidirect

Maximal subgroups

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

subgroupindex
#214572582
#214480342
#214473992
#214438112
C61×#13282
#1230461