Finite Group Databasebeta

← #29593372

Subgroups — #29593372

Order 15616.

286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448031C212yesmaximal, complemented
2#21447399C211yesmaximal, characteristic, complemented
3#21443810C212yesmaximal, complemented
4#21443772C211yesmaximal, characteristic, complemented
5C61×#3259C211yesmaximal, characteristic
6#16839811C2211yescharacteristic
7#16839584—22no—
8#16839575—22no—
9#16839544C2212yes—
10#16839532—21no—
11#16839527—21no—
12#16839520C2211yescharacteristic
13C61×#540—21no—
14C61×#478—22no—
15C61×#469C2212yes—
16C61×#466—21no—
17C61×#459—22no—
18C61×#424C2211yescharacteristic
19C2×#11758194—21no—
20C2×#11758194—21no—
21#14519717—22no—
22#14519713—22no—
23C2×D8×C61—21no—
24C2×D8×C61D412yes—
25C2×M16×C61C2311yescharacteristic
26C22×C8×C61D411yescharacteristic
27#127×C61—21no—
28#125×C61—21no—
29#123×C61—42no—
30#121×C61—22no—
31#121×C61—42no—
32C4×D4×C61—22no—
33#117×C61D411yescharacteristic
34#107×C61—21no—
35#106×C61D412yes—
36C4⋊C8×C61—22no—
37#102×C61—22no—
38#102×C61—22no—
39C2×D4×C61—22no—
40C2×D4×C61—42no—
41C2×D4×C61—42no—
42C22×C4×C61—42no—
43C22×C4×C61C2×D411yescharacteristic
44D8×C61—42no—
45D8×C61—81no—
46M16×C61—41no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49C2×C8×C61C2×D412yes—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—42no—
53C22⋊C4×C61—42no—
54C22⋊C4×C61—42no—
55C22⋊C4×C61SD1612yes—
56C42×C61—21no—
57#11758194—41no—
58#11758194—41no—
59#11758194—41no—
60#11758194—41no—
61C2×#92418—41no—
62C2×#92418—41no—
63#11758185—42no—
64C23×C61—42no—
65C23×C61C2×SD1611yescharacteristic
66D4×C61—42no—
67D4×C61—42no—
68D4×C61—162no—
69D4×C61—162no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—42no—
74C2×C4×C61—162no—
75C2×C4×C61#12011yescharacteristic
76C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
77C8×C61—22no—
78C8×C61—41no—
79#92418—81no—
80#92418—81no—
81#12304—611nomaximal, Sylow
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—82no—
85C22×C61—82no—
86C22×C61—82no—
87C22×C61#45011yescharacteristic
88C4×C61—21no—
89C4×C61—42no—
90C4×C61—82no—
91C4×C61#45411yescharacteristic
92C4×C61#45811yescharacteristic
93#3259D6111yescharacteristic
94#2238—612no—
95#2103—611no—
96#1341—612no—
97#1328—611no—
98C2×C61—21no—
99C2×C61—41no—
100C2×C61—162no—
101C2×C61#161611yescharacteristic
102#540—21no—
103#478—22no—
104#469C2×D6112yes—
105#466—21no—
106#459—22no—
107#430—611no—
108#424C2×D6111yescharacteristic
109#365—1222no—
110#361—1222no—
111#349—612no—
112#344—1221no—
113#341—1221no—
114#338—611no—
115C61#1230411yescharacteristic, complemented, Sylow
116C2×D8—21no—
117C2×D8C22⋊D6112yes—
118C2×M16—1221no—
119C2×M16—1221no—
120C2×M16C22×D6111yescharacteristic
121C22×C8C22⋊D6111yescharacteristic
122#127—21no—
123#125—21no—
124#123—42no—
125#121—22no—
126#121—42no—
127C4×D4—22no—
128#117C22⋊D6111yescharacteristic
129M32—1222no—
130#108—1222no—
131#107—21no—
132#106C22⋊D6112yes—
133C4⋊C8—22no—
134#102—22no—
135#102—22no—
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—42no—
139C22×C4—42no—
140C22×C4C2×C22⋊D6111yescharacteristic
141D8—42no—
142D8—81no—
143M16—41no—
144M16—2441no—
145M16—2441no—
146M16—2441no—
147M16—2441no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—2441no—
151C2×C8—2441no—
152C2×C8C2×C22⋊D6112yes—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C22⋊C4—42no—
158C22⋊C4#1175820012yes—
159C42—21no—
160C16—2442no—
161C23—42no—
162C23C2×#1175820011yescharacteristic
163D4—42no—
164D4—42no—
165D4—162no—
166D4—162no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—162no—
172C2×C4#1451974611yescharacteristic
173C2×C4#1451980311yescharacteristic
174C8—22no—
175C8—41no—
176C8—4881no—
177C8—4881no—
178C22—21no—
179C22—41no—
180C22—82no—
181C22—82no—
182C22—82no—
183C22#1683991311yescharacteristic
184C4—21no—
185C4—42no—
186C4—82no—
187C4#1683993511yescharacteristic
188C4#1683995211yescharacteristic
189C2—21no—
190C2—41no—
191C2—162no—
192C2#2144485611yescharacteristic
subgroupG/H
centerC2#21444856
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
Fitting, prime radicalC61×#3259C2
socleC2×C61#1616
hypercenter#3259D61
hypocenterC61#12304
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3259

Complements

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

NH ≅ G/Ntype
1. #21448031C2semidirect
2. #21447399C2semidirect
3. #21443810C2semidirect
4. #21443772C2semidirect
115. C61#12304semidirect

Maximal subgroups

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

subgroupindex
#214480312
#214473992
#214438102
#214437722
C61×#32592
#1230461